Cheers rang around Etihad Stadium after second-half goals from Jeremy Doku, Erling Haaland and Omar Marmoush helped second-placed City close the gap on leader Arsenal to two points.
But it was a very different atmosphere at Anfield where Liverpool fans jeered as the defending champions dropped more points in a 1-1 draw with Chelsea.
Another big goal from Doku settled City nerves and kept manager Pep Guardiola in contention for a seventh Premier League title.
A well-organised Brentford managed to frustrate City until Doku came up with a moment of magic on the hour — curling a right-footed shot into the far corner.
It was a near-carbon copy of his late equaliser against Everton that salvaged a 3-3 draw for Guardiola's team on Monday.
That draw put the title race in Arsenal's hands, but victory against Brentford ensured the pressure remained on the Gunners to get a win at West Ham on Sunday.
Haaland bundled the ball over the line in the 75th for City's second and his 50th of the season for club and country, before substitute Marmoush got the third in added time.
Liverpool's draw saw them move a step closer to guaranteed Champions League qualification — fourth in the table with two rounds left — but another unconvincing performance sparked a frustrated reaction from the crowd.
There were boos at the final whistle to mark growing unrest from Liverpool supporters in a season when they've tamely surrendered the title despite spending around $A786 million in the transfer market.
"This season the fans will have their opinion and it will not change, but if we can have the summer that we are planning to have I am 100% convinced we will be a different team next season," said under-pressue manager Arne Slot.
Liverpool can make certain of a place in the Champions League with a victory at Aston Villa next Friday.
Chelsea ended their six-game losing streak, with Enzo Fernandez's bouncing free kick going in before halftime for the equaliser after Ryan Gravenberch's early goal.
Elsewhere, third-placed Manchester United drew at Sunderland 0-0 while there were wins for Champions League-chasing Bournemouth and Brighton.
Sixth-placed Bournemouth won at Fulham 1-0 in a game in which both teams were reduced to 10 men, while seventh-placed Brighton beat bottom club Wolves 3-0, with a goal after 35 seconds from Jamie Hinshelwood being the fastest Seagulls strike ever in the Premier League.
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