The result moved Pep Guardiola's side to within two points of leaders Arsenal, who were preparing to face relegation-threatened West Ham United on Sunday in a bid to restore their five-point cushion at the summit.
After being held to a dramatic 3-3 draw by Everton earlier in the week, City responded emphatically with three second-half goals against a stubborn Brentford side that had created problems throughout the opening period.
Jeremy Doku was City's standout performer from the beginning. The Belgian nearly struck inside two minutes before forcing Brentford goalkeeper Caoimhin Kelleher into a sharp low save.
He also supplied a teasing cross that Erling Haaland headed wide, while another Haaland effort was blocked by Kristoffer Ajer.
Despite City's pressure, Brentford threatened from set-pieces and long throws. Gianluigi Donnarumma endured an anxious moment when Michael Kayode launched a dangerous throw into the area, with the ball eventually cleared off the line.
Mathias Jensen also tested the Italian with a curling free-kick, while Igor Thiago was denied at the near post after the interval.
City finally broke through around the hour mark when Doku cut inside and curled a superb finish into the far corner, echoing the late strike he scored against Everton on Monday.
Haaland doubled the lead with 15 minutes remaining before substitute Omar Marmoush added a late third goal to secure Donnarumma's clean sheet.
Pep Guardiola has said he will make a late decision on the fitness of Rodri and Abdukodir Khusanov ahead of Manchester City's crucial Premier League clash with Crystal Palace on Wednesday night.
Manchester City manager Pep Guardiola believes Jeremy Doku has the potential to reach the level of top wingers such as Vinicius Junior and Lamine Yamal after the Belgian continued his impressive scoring run in Saturday's 3-0 win over Brentford.
Pep Guardiola believes Phil Foden will return to his best once he rediscovers the joy that made him one of the Premier League's most exciting talents, insisting the Manchester City midfielder is going through a temporary phase rather than a decline.
Pep Guardiola is hopeful that Manchester City could be boosted by the return of Rodri for Saturday's Premier League clash with Brentford at the Etihad Stadium, as the champions look to keep pressure on Arsenal in a tense title race.
