This result lifted the Reds, who have endured a tough start to their season, to eighth in the table and left the Sky Blues four points off leaders Arsenal, who won 1-0 at Leeds United earlier in the day.
Needless to say, there was so much more to this than the result.
There was quality aplenty and intriguing contrasts offered by both sides – sides who have so often set the standard for English, and arguably European, football over the last five years or so.
And there was, almost inevitably, controversy. City saw a goal disallowed via VAR early in the second half after Erling Haaland was adjudged to have fouled Fabinho in the moments prior to the striker knocking the ball away from goalkeeper Alisson Becker in the box and Phil Foden converting the loose ball.
Klopp was also red-carded by referee Anthony Taylor in the latter stages after he berated the assistant referee for not penalising Bernardo Silva for an apparent foul on Salah.
The defining moment, though, came as Alisson’s brilliant long-range pass was preceded by Salah’s wonderful turn and finish.
Story of the match
Both Klopp and Guardiola made five personnel changes from their respective midweek Champions League away trips.
Following Liverpool’s emphatic 7-1 win at Rangers on Wednesday, Ibrahima Konaté, who was absent through a muscle issue, Kostas Tsimikas, Jordan Henderson, Fábio Carvalho and Darwin Núñez made way, as James Milner, Andy Robertson, Thiago Alcântara, Salah and Diogo Jota came in.
For City, meanwhile, Aymeric Laporte, Sergio Gómez, Riyad Mahrez, Jack Grealish and Julián Álvarez each dropped to the bench after starting Wednesday’s 0-0 draw with FC Copenhagen. That saw Rúben Dias, Nathan Aké, Bernardo Silva, Foden and Haaland come in.
The contest opened with a familiarly lively tempo, before it settled into a slightly gentler rhythm with City having the majority of the ball.
It was the 15th minute when the first effort of note arrived, as İlkay Gündoğan saw a 25-yard volley well-gathered by Alisson.
Then the hosts worked some openings. First, in the 20th minute, Salah fended off Aké as he burst forward and into the visitors’ box before Dias intervened to divert the ball behind for a corner.
Then, from that corner, Elliott picked up the second ball and floated a cross to the far-post which Jota headed on-target but into the gloves of Ederson.
Shortly after that, the Reds’ best move of the match thus far saw Virgil van Dijk’s switch to Milner open up the game and give Fabinho the chance to then play the 36-year-old in behind.
Milner’s cross was an inviting one and forced Ederson to palm it away on the dive. Robertson latched onto the loose ball but the Scotland skipper drilled a powerful half-volley over.
Even so, things were heating up encouragingly.
Back came City.
Bernardo Silva – who often looked to be operating within a double-pivot in midfield alongside Rodri – rifled a 30-yard effort over in the 30th minute, before Premier League top-scorer Haaland had his first real chance in the 33rd.
The Norwegian was cleverly slid in behind and looked to dink a finish over the advancing Alisson who did well to stand tall and palm it away.
Then, the 22-year-old was twice teed-up with typical class by Kevin De Bruyne.
He headed a 35th-minute volleyed delivery narrowly over before he nodded a more presentable chance into the gloves of Alisson.
Half-time came and went and then, similarly to last year, the contest began to click into higher gears.
Five minutes after the restart, Salah span and was sent through by a clever Roberto Firmino pass, but his left-footed shot was superbly tipped wide by Ederson. The fineness of the margins was highlighted by the fact that Taylor gave a goal-kick rather than a corner.
Then, after Ederson had received some treatment for a knock, it briefly appeared that City had the lead.
Haaland held off Fabinho and, soon after, raced onto a De Bruyne pass to poke it away from Alisson as the goalkeeper attempted to gather it. Foden then converted the loose ball despite Joe Gomez’s best efforts on the line.
However, a check of the VAR screen saw Taylor disallow the goal for Haaland’s shirt pull on Fabinho.
Guardiola and City, somewhat understandably, weren't best pleased.
The atmosphere and the game duly stepped up another few notches.
Within moments, Salah floated a sublime cross to the far-post and into the path of the unmarked Jota but the Portuguese forward sent his diving header just wide.
The 64th minute brought another opening for Haaland as he saw a sidefooted effort pushed away by Alisson, and Bernardo Silva and Salah both saw low attempts skid narrowly wide in the following five minutes.
Then, in the 76th minute, came the match’s decisive moment. And it was some moment.
After a City free-kick was gathered by Alisson, he looked up, saw Salah, and pinged a superb 70-yard volleyed pass towards the Egyptian.
In one motion, the No.11 controlled the ball on the bounce with his right foot, rolled away from João Cancelo and put himself one-on-one with Ederson.
This time, he put some air on his left-footed finish to lift it over the advancing goalkeeper and into the bottom-left corner.
He wheeled away and stared deep into the delirious Kop.
A fourth goal of the week for him, following his record-breaking hat-trick at Rangers. A third Liverpool assist for Alisson, who previously teed-up Salah against Manchester United in January 2020 and against Norwich City in February 2022.
A goal worthy of winning the game. But there was still plenty of work to do, as was to be expected with City around.
Núñez – introduced as part of a 73rd-minute triple substitution – was next to come close, though, as he drove forward and whipped an effort narrowly wide.
But the visitors were building pressure. Only a superb header over his own crossbar by Van Dijk prevented Haaland latching onto a volleyed Cancelo cross in the six-yard box in the 82nd minute before Gündoğan saw a cross-shot well held by Alisson.
Klopp was red-carded by Taylor in the 86th after he berated the assistant referee, seemingly for not flagging for a foul after Salah appeared to have been dragged down by Bernardo Silva.
It was a challenge and a subsequent passage of frustration that reflected the relentlessness and physicality of much of the contest.
City kept pushing, but the remaining chances of note fell to the hosts.
All of which involved Núñez, who offered a superb outlet in the latter stages – even if some of his decision-making could have been better.
The 88th minute saw him lead an advance into the City half but fail to square to the unmarked Salah.
The third minute of stoppage time saw him burst into the box from the left and find the newly introduced Trent Alexander-Arnold at the far-post, who couldn’t quite convert on the stretch.
Then, three minutes after that, he was played through and lifted the ball over Ederson but not with enough pace to prevent Aké from clearing.
A considerable stoppage followed as Jota was stretchered off with what appeared to be a muscular injury, but the Merseysiders saw out the remaining seconds assuredly to secure a hard-fought, crucial victory.
Second-half step-up
It wasn’t surprising, but things became considerably more intense after half-time.
The tempo. The atmosphere. The level of feeling.
All had been bubbling nicely throughout the opening 45 but, with City’s disallowed goal and the chances that followed at both ends, the second half offered a wonderful level of intrigue and adrenaline.
The margins were fine, the levels required felt as high as in virtually any game so far in 2022/23 and it always felt likely that a moment of considerable class would decide the contest – which proved the case.
Player of the match: Mo Salah
There were several contenders in this regard. Gomez – who won Sky Sports’ player of the match award – and Van Dijk were superb in their focus and discipline at centre-back.
Milner was brilliantly balanced in his approach at right-back – after he struggled in that position in this fixture last season – while Foden and Bernardo Silva regularly caught the eye for the visitors.
Salah, though, led the line excellently from the off. Playing as the most advanced central forward in a 4-2-3-1, he regularly occupied centre-backs Dias and Aké, offered that familiar threat in-behind and timed his drifts to the right flank well, too.
After being denied brilliantly by Ederson once, he kept plugging away in typical fashion and then crafted and converted the winner sublimely.
