Liverpool won a seventh straight game in all competitions from the start of a season for the first time in 28 years by easing past Southampton at Anfield.
The hosts scored three first-half goals to subdue Saints into just limiting the damage after the break and Reds boss Jurgen Klopp said the challenges will get "tougher and tougher" for his side.
"I wasn't interested in the history before the game but now I like it," the German told BBC Sport.
"We will try to carry on that path but it's unbelievable what is coming up now."
In their next four matches, Liverpool face Chelsea twice, travel to Napoli and then host Premier League champions Manchester City.
"The boys are in good shape. That helps - let's see if we can carry on," added Klopp.
On Saturday, the hosts took the lead after 10 minutes when Xherdan Shaqiri's shot deflected off Shane Long and then Wesley Hoedt for a peculiar own goal.
Joel Matip rose above opposing centre-back Jannik Vestergaard to head in Trent Alexander-Arnold's corner and double the advantage.
Liverpool added a third just before the break as Shaqiri's superb free-kick came down off the crossbar and Mohamed Salah turned the ball in from close range.
Saints were not quite as poor as being three down at half-time suggests. However, they sat back in the second half, perhaps content not to be embarrassed - though Salah did have a goal disallowed for offside late on.
Klopp's side go back to the top of the Premier League with their sixth straight win in the competition, and they also beat Paris St-Germain in their Champions League opener on Tuesday.
Liverpool won eight straight league games and 10 in all competitions from the start the 1990-91 season.
Three and easy
The second half of this game felt like an extra training session for both sides given how emphatically Liverpool's first-half spree had ended the match as a contest.
Their opener was fortuitous but did originate from Sadio Mane's superb pass to pick out Shaqiri on the left before the Swiss - who was making his first Liverpool start - cut back onto his right and tried to pick out the far corner.
Long blocked the strike but Hoedt could not prevent the deflection rebounding off his thigh and past the scrambling Alex McCarthy.
Mane, Salah and Roberto Firmino - making his full return after an eye injury - scythed through Southampton at times but could not quite find the decisive final touch, with Salah denied by a fine Cedric Soares tackle after a one-two with Firmino.
But if the Reds' poise was slightly off, the power was not - Matip thumping a header into the top of the net from the corner that followed Cedric's intervention.
Shaqiri was then denied by the crossbar after beating McCarthy from 25 yards with a sublime, dipping free-kick, but Salah was sharp enough to get to the rebound first and score his third of the season.
Sterner tests await
Aside from the 4-0 thrashing of West Ham on the opening weekend, this was perhaps the easiest win of Liverpool's record run and Saints' complete indifference to chasing the game in the second half afforded the hosts welcome comfort after the frenetic 3-2 win over PSG.
The only real moment of concern was when Virgil van Dijk, solid in defence whenever his former side did foray forward, had to come off after being struck in the torso, though Klopp said after the game the injury is not serious.
"Before the PSG game, he already had kind of a bruised rib, which is very uncomfortable, and he got another hit there," said the German.
Liverpool next face Chelsea back to back in the Carabao Cup and Premier League, before travelling to Napoli in the Champions League and then hosting champions Manchester City in the league on 7 October.
Those opponents, not an insipid Southampton, will give a better indication of how strong this Reds side are.
Spiritless Saints
Southampton were unlikely ever to try and steamroller Liverpool but they were limited by Danny Ings being unable to play against his parent club and fellow forward Manolo Gabbiadini ruled out with a hamstring problem.
Instead it was left to Long, who has now scored just twice in his past 52 appearances, to lead the line and the Republic of Ireland striker was isolated for long periods.
They did create openings - Nathan Redmond got in behind down the right several times, while Ryan Bertrand picked out Pierre-Emile Hojbjerg unmarked in the area, only for the Denmark midfielder to scuff his effort.
Yet it took until the 91st minute for Saints to have a shot on target when substitute Charlie Austin struck straight at Alisson.
Ultimately, that unlucky own goal and Vestergaard's mistake in allowing Matip to get above him for the second killed any interest Mark Hughes' side had in challenging a clearly superior side.
They sat deeper and deeper as the second half wore on, more reminiscent of a side protecting a 1-0 lead than trying not to concede a fourth - and they almost failed in that endeavour too, but Salah came back from an offside position to turn in James Milner's blocked shot.
Man of the match - Xherdan Shaqiri (Liverpool)
'Not a good day for us' - reaction
Liverpool manager Jurgen Klopp talking to BBC Sport: "My plan was to change tactics but we didn't have time to train because of the weather in Liverpool.
"In the second half we had to control the game and it wasn't the most exciting football anymore but we were still good enough to be the deserved winner."
Southampton manager Mark Hughes, talking to BBC Sport: "We conceded too readily in the first half. Clearly you don't want to do that against a very good Liverpool team at home.
"We were guilty of not stopping them creating moments in the first half. The second half was damage limitation. The guys were better in terms of shape, stopped some good attacks and got a clean sheet in the second half.
"We won't be the first team and we won't be the last that this has happened to. I'm pleased we were a little more controlled in the second half. We will take that positive - but overall not a good day for us."
Klopp dominates Hughes again - match stats
- Klopp has won all five of his Premier League meetings with Hughes, more than he has against any other manager in the competition.
- Southampton manager Mark Hughes has lost his past six league games against Liverpool by an aggregate score of 17-3.
- Liverpool have won their first six games of a top-flight season for the third time, after doing so in 1978-79, when they finished first, and 1990-91, when they were second.
- The Reds are unbeaten in their past 24 league matches at Anfield, winning 16 - their best run in the competition since August 2009 (31 games).
- Salah has been directly involved in 41 goals in 31 games for Liverpool at Anfield (30 goals, 11 assists).
- Klopp took charge of his 600th league game in his managerial career - he has won 296, drawn 158 and lost 146.
What's next?
Liverpool host Chelsea in the EFL Cup third round on Wednesday (19:45 BST) before travelling to the Blues in the league on Saturday, 29 September (17:30 BST), with Saints away at Wolves on the same day at 15:00 BST.
Line-ups
Liverpool
Formation 4-2-3-1
13Alisson
66Alexander-Arnold32Matip4van Dijk26Robertson
5Wijnaldum14Henderson
10Mané23Shaqiri9Firmino
11Salah
- 13Alisson
- 66Alexander-Arnold
- 32Matip
- 4van DijkSubstituted forGomezat 55'minutes
- 26Robertson
- 5WijnaldumSubstituted forKeitaat 70'minutes
- 14Henderson
- 10Mané
- 23ShaqiriSubstituted forMilnerat 45'minutes
- 9Firmino
- 11Salah
Substitutes
- 3Fabinho
- 7Milner
- 8Keita
- 12Gomez
- 15Sturridge
- 18Moreno
- 22Mignolet
Southampton
Formation 4-1-4-1
1McCarthy
2Cédric Soares4Vestergaard6Hoedt21Bertrand
14Romeu
22Redmond23Højbjerg18Lemina33Targett
7Long
- 1McCarthy
- 2Cédric Soares
- 4Vestergaard
- 6Hoedt
- 21Bertrand
- 14RomeuBooked at 34minsSubstituted forBednarekat 55'minutes
- 22Redmond
- 23Højbjerg
- 18LeminaBooked at 56mins
- 33TargettSubstituted forS Armstrongat 55'minutes
- 7LongSubstituted forAustinat 79'minutes
Substitutes
- 3Yoshida
- 8Davis
- 10Austin
- 16Ward-Prowse
- 17S Armstrong
- 28Gunn
- 35Bednarek
Referee:Paul Tierney
Attendance:50,965
Match Stats
Live Text
Match ends, Liverpool 3, Southampton 0.
Second Half ends, Liverpool 3, Southampton 0.
Offside, Liverpool. Sadio Mané tries a through ball, but Mohamed Salah is caught offside.
Corner, Southampton. Conceded by Alisson.
Attempt saved. Charlie Austin (Southampton) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by Cédric Soares.
Offside, Liverpool. Roberto Firmino tries a through ball, but Mohamed Salah is caught offside.
Attempt blocked. James Milner (Liverpool) left footed shot from the centre of the box is blocked.
Attempt blocked. James Milner (Liverpool) right footed shot from the centre of the box is blocked.
Mohamed Salah (Liverpool) wins a free kick in the attacking half.
Foul by Jannik Vestergaard (Southampton).
Attempt missed. Andrew Robertson (Liverpool) left footed shot from the centre of the box is just a bit too high following a corner.
Corner, Liverpool. Conceded by Jan Bednarek.
Substitution, Southampton. Charlie Austin replaces Shane Long.
Foul by Roberto Firmino (Liverpool).
Cédric Soares (Southampton) wins a free kick in the defensive half.
Foul by Mohamed Salah (Liverpool).
Wesley Hoedt (Southampton) wins a free kick on the left wing.
Substitution, Liverpool. Naby Keita replaces Georginio Wijnaldum.
Joel Matip (Liverpool) wins a free kick in the defensive half.
Foul by Shane Long (Southampton).
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