Pep Guardiola’s men went back to the top of the table with a 2-0 win that piled the pain on Manchester United.
Bernardo Silva broke the stalemate on 54 minutes, before substitute Leroy Sane broke United hearts with a second soon after.
City have now won 11 straight games to lead Liverpool by one point with three matches to go.
Guardiola ordered his stars to go to sleep and keep calm ahead of the final run in.
“We are still not champions with three games left”
He said: “It’s important to be calm. We are still not champions with three games left – it’s incredible with the points we have and Liverpool have and I have the ultimate respect for my team.
“I told the players don’t read tomorrow, don’t watch the television, just rest and sleep a lot and go in there against Burnley.
“Both teams deserve the title. But it can be just one. The team that is going to lose can’t have regrets because they have given everything.
“Normally with this kind of victory you can it enjoy it the most – but we have to be calm.”
Home fans headed for the exits long before the end as United crashed to their seventh defeat in nine games for the first time since 1962.
Solskjaer was taunted with chants of ‘you’re getting sacked in the morning’ from travelling supporters as the clock ticked down.
United striker Marcus Rashford hit out at his side and insisted the dramatic slump was unacceptable.
He said: “We didn’t play like Manchester United. It’s not right. The bare minimum is to work hard and give all for the badge, the supporters, the club and yourself.
“It has been a tough road to get to where we are, to get there and not be putting up the same performances as we were in January is disappointing.
“We know what’s been going wrong, it’s mentality and willingness to run for your team.
“Forget the league and top four, you don’t lose this game. It’s that simple as a Manchester United fan.
“We never call each other out – but we have to be real with each other. It’s a matter of trying to improve each other.
“We have to get to the bottom of it and start playing like Manchester United for ourselves.”