City were condemned to a third straight defeat for the first time in Guardiola's near two-year reign 13 minutes from time when Otamendi was caught in possession and Firmino slotted in off the far post to the delight of the Liverpool fans gathered behind Ederson's goal.
In Manchester, Egypt striker Salah struck with a neat left-foot chip in the 56th minute to stun City who dominated the first half and led from an early goal, but had manager Pep Guardiola sent to the stands as the teams came off at the break. There is a reason an orchestra has a conductor.
The Reds, who were smothered and on the ropes for much of the first half, sealed their qualification to the semi-final with two second half goals from Roberto Firmino and Mohamed Salah, canceling out Gabriel Jesus' second-minute opener for the hosts.
Many teams have big decisions go against them, and Manchester City have had their fair share this week, but it is how sides react to those decisions that really define them.
Had Sane's goal not been disallowed, City would have jumped 2-0 in front of the night. Follow all the action as it happens. "We didn't get high enough, didn't get the pressure on them and that's as a team, everyone together, so I thought we did that, we got about them a bit more second half".
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"In this competition you have to make it ideal and the decisions have to be good". If we gave them those second balls, they were already in the right place to make three or four passes.
It was a total turnaround of the first leg as City were the dominant team on this occasion as Liverpool were forced to sit back fending off all the attacking threat. "I was not overly happy at halftime to be honest", said Klopp.
Manchester City, having now lost three in a row in all competitions, travel to Tottenham on Saturday - live on Sky Sports - but they must win and hope Manchester United slip up at West Brom to finally seal the title.
In the end, Liverpool went through 5-1 on aggregate, and Guardiola said it was a deserved result.
One area of hope for Guardiola is that Liverpool's Achilles heel has been their defence, although Dutchman Virgil van Dijk has added some steel since joining from Southampton in January.
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"Everyone knows how good Manchester City are so to beat them is a good confidence builder", said the former City player.
We have to be flawless, Guardiola kept on saying in the buildup, despite the creeping suspicion that being flawless, aiming each time for the ideal realisation of pure, unfettered Pep-ball might be part of the problem.
His team started in a similar manner to how Liverpool had played the previous Wednesday.
"City took all the risks they could take".
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It is true, however, that jobs that have been historically dominated by women are paid less than jobs that are dominated by men. Chris Christie, who said existing safeguards protected against unequal pay for the same work.
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