Alexandre Lacazette capitalised on Andrew Robertson's mistake to give Arsenal a surprise lead on 25 minutes, but Sadio Mane swiftly restored parity before Robertson made amends for his error to give the Reds a deserved half-time lead.
Lacazette spurned a glorious chance to draw an improved Arsenal level midway through the second half and his miss was compounded on 88 minutes when summer signing Diogo Jota's first goal for the club sealed a third straight win of the season for Jurgen Klopp's side.
The result lifts the champions above Merseyside rivals Everton on goal difference into second in the Premier League, while Arsenal remain fifth after tasting defeat for the first time.
Liverpool: Alisson (8), Alexander-Arnold (8), Gomez (7), Van Dijk (7), Robertson (7), Fabinho (6), Wijnaldum (6), Keita (6), Mane (8), Salah (7), Firmino (6).
Subs: Milner (5), Jota (7), Minamino (n/a).
Arsenal: Leno (7), Holding (6), Luiz (7), Tierney (6), Bellerin (5), Elneny (6), Xhaka (6), Maitland-Niles (6), Willian (5), Lacazette (6), Aubameyang (5).
Subs: Ceballos (6), Pepe (5), Nketiah (5).
Man of the Match: Sadio Mane.
How Liverpool stayed perfect after Lacazette scare
Liverpool were dominant from the outset, with Trent Alexander-Arnold back to his creative best as the hosts applied constant pressure on the Arsenal goal.
The returning David Luiz scrambled a Virgil van Dijk header out of the Arsenal goalmouth after the Dutchman reached Alexander-Arnold's deep cross, and on the quarter-hour mark the right-back picked out Mane, but his sweeping shot was straight at Bernd Leno.
- Joe Gomez returned, replacing Jordan Henderson in Liverpool’s only change from the win at Chelsea. Fabinho pushed forward to fill the vacant midfield berth, while summer signing Thiago Alcantara was absent from the squad.
- Kieran Tierney, David Luiz, Mohamed Elneny and Ainsley Maitland-Niles returned as Arsenal made four changes to the side that beat West Ham last weekend. Gabriel Magalhaes dropped to the bench.
The woodwork came to the Gunners' rescue on 21 minutes, denying Alexander-Arnold the opening goal after his drive from the edge of the box deflected off Hector Bellerín.
The element of luck that underpinned Arsenal's containment of the champions came to the fore on 25 minutes when their first attack yielded a gift-wrapped opening goal.
Robertson made a mess of dealing with Pierre-Emerick Aubameyang's hopeful cross, scooping a clearance straight to Lacazette, whose scuffed effort found a way past Alisson.
Liverpool's response was instant. Mohamed Salah drove into the area, held off the challenge of Kieran Tierney and got a shot away which Leno could only parry into the path of Mane, whose close-range tap-in drew the Reds level 147 seconds after they fell behind.
Seven minutes later and Liverpool had the lead. Another Alexander-Arnold cross was on the money, reaching fellow full-back Robertson who chested the ball down and poked a shot home to atone for his earlier error.
Gunners boss Mikel Arteta used the interval to issue fresh instructions to his players, and the visitors were markedly improved in the second period, having been given licence to push further forward.
Either side of Leno saving Van Dijk's low drive, Lacazette was twice clean through. He was eventually found offside for the first, but his finishing was found wanting on both occasions against the imperious on-rushing Alisson.
Lacazette nearly lived to rue the miss instantly, with Mane's shot on the swivel flashing just wide of the Arsenal goal.
Arsenal dug in and refused to crumble like they had in the past at Anfield, but the Liverpool pressure finally told as substitute Jota controlled and volleyed in his first goal for the club to put the seal on the victory.
Klopp responds to Keane: We were not sloppy!
Jurgen Klopp described Liverpool's performance as "exceptional" after taking issue with Roy Keane using the word "sloppy" in his analysis.
Reds boss Klopp overheard pundit Keane giving his assessment in the Monday Night Football studio as he waited to be interviewed at the side of the Anfield pitch.
"Did I hear right that Mr Keane said we had a sloppy performance tonight, because I could hear you already?" Klopp told Sky Sports.
"Did he say that? This was a sloppy performance tonight? Maybe he spoke about another game. It cannot be this game, sorry. That's an incredible description of this game.
"This was absolutely exceptional. Nothing was sloppy, absolutely nothing. It was, from the first second, dominant against a team in form, 100 per cent in form. About this game tonight, there is nothing bad to say."
What the managers said…
Liverpool manager Jurgen Klopp: "We had so many big moments but I know we can't finish off every chance, but we played a super game and were 1-0 down. It would've been incredible had we lost but we won, and it's completely deserved.
"Could we have scored more goals? Yes. Could they have scored? Yes, because of the quality that they have. We played a constant high line. We stuck to the match plan and if you are that high, of course there is a risk.
"We like to try to win the ball back as high as possible, so I wasn't frustrated or disappointed. I was in the game, and it could've gone either way.
"We had to be brave ourselves to cause them problems - that's what we tried and sometimes it worked. We didn't stop, and my worry was at half-time that we couldn't keep it going but we did and that's a really good sign."
Arsenal head coach Mikel Arteta: "It's a tough place to come for anybody in the world. They set incredible standards, they dominate every aspect of the game.
"Taking the lead put us in a really strong position to believe more that we could get something out of the game. We conceded too early, in a mistake.
"In the second half we corrected a few things, we were much better. We had some problems still with the ball and we had the best chance in the game and when it comes to Anfield you're not going to get 10 chances.
"When you get through one against one against the keeper, you have to score if you want to get something out of the game."
Opta stats - Arsenal's Anfield woes continue
- Liverpool have won their last five home league games against Arsenal, their longest such run against them since a run of seven between 1981-1988.
- Since Mikel Arteta's first game in charge in December 2019, Arsenal have dropped more points from winning positions than any other side in the Premier League (18).
- There have been 166 goals scored in Premier League meetings between Arsenal and Liverpool, at least seven more than any other fixture in the competition.
- Diogo Jota became the 13th player to score on his Premier League debut for Liverpool, and the first to do so in a match against Arsenal since Sadio Mané in August 2016.
- Andrew Robertson has scored (2) or assisted (5) a goal in seven of his last eight Premier League games for Liverpool, failing only against Chelsea in this run.
- Sadio Mané has scored in four of his five home league games against Arsenal for Liverpool, with his equaliser today coming just 147 seconds after the Gunners had taken the lead.
- Alexandre Lacazette has scored six goals in his last nine Premier League games, while he became the first player to score in each of Arsenal's first three league games in a season since Olivier Giroud in 2013-14.
Arsenal return to Anfield for a fourth-round Carabao Cup tie against Liverpool on Thursday at 7.45pm
On Super Sunday, Arsenal host Sheffield United at 2pm before Liverpool travel to Aston Villa at 7.15pm - both live on Sky Sports Premier League.
Source: Sky Sports / Jack Wilkinson