Headers from De Bruyne and Jesus made it 2-0, Gabriel tapped in a third and Zinchenko's curler put City four up.
Gabriel added two more headers, with Foden, Walker and Mahrez also scoring.
This was the first time in more than 21 years that City had scored more than eight goals in a single match - they beat Huddersfield Town 10-1 in a second-tier league encounter in November 1987.
It means City have scored 16 goals in four days after thrashing Rotherham United 7-0 in the third round of the FA Cup on Sunday.
Gabriel said, "I have never scored four before in my career, I am so happy for this. We played very well and with respect, that's important.
"Players like me want to play more, to help the team, and we went out there to win."
Zinchenko added: "It's the first time I've played in a win like this. To be fair we scored a lot of goals, we wanted more, and our fans did too.
"We wished we could get 10, maybe next time. Was my goal a cross?! A little respect please...
"At half time Pep (Guardiola) said keep going in the same way, the same spirit and if we can score more."