The 28-year-old midfielder - who earns £100,000 per week as salary, according to Spotrac.com - started the game and played for the entire 90 minutes, as it ended in a goalless draw.
However, the game could have been lost right at the end were it not for a bad penalty kick miss from new Manchester City signing Riyad Mahrez, who skied his spot-kick after Leroy Sane was felled in the area by Leroy Sane.
As for what it means for the standings, there is now a three-way tie for first with teams having records of 6-2-0.
Liverpool's front three had been deadly in those Anfield games last season but they created little on Sunday, with the home side's rhythm further disrupted by a first-half injury to James Milner. Instead, he skied it and cost his team a historic win at Anfield.
"We were lucky in that situation but we deserved it, a bit of luck, because with the performance the boys showed today, it's just good", he said.
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"He did not start in the first 11 today but when he was on he scored within a minute and that gives confidence for both him and us". They now sit level at the top of table, with Chelsea, on 20 points after eight games of the season.
City's normal penalty taker, Sergio Aguero, had already been substituted when Virgil van Dyke clattered into Leroy Sane in what the defender later admitted was "not a smart move". And we hope that they come back healthy and play these easy competitions, the Premier League, the Champions League and all this.
"When I was up there in the commentary box, I could see the goalkeeper coach, you can see what he's telling him", the Liverpool legend said on Sky Sports.
"Not struggling in the sense of playing badly but I felt as though Liverpool just had the edge on them when I was watching".
Liverpool were tipped as the main contenders for defending champions City in the build up to the campaign and have lived up to the billing so far. "It looks like they are in a good shape", said Klopp.
Blues boss Maurizio Sarri has talked about there being a gap between his team and City and Liverpool, but they can close it if they can keep Hazard fit and in the kind of form he is in at the moment. I thought how we defended was brilliant. I made the decision to shoot in the middle - the ball went up.