Second-half goals from Juan Mata, Oscar, Lampard and John Terry secured Chelsea a fifth round tie at Championship (second division) Middlesbrough on Feb. 27.
Chelsea twice had to come from behind to earn a 2-2 draw in their first encounter at Griffin Park and were again sluggish in the first half against their fellow Londoners.
Mata finally broke Brentford's resistance on 54 minutes when he latched on to Demba Ba's flick from a long Petr Cech clearance and drilled in a left-foot shot from 20 metres.
Oscar doubled the lead 14 minutes later from Branislav Ivanovic's cutback, scoring with a deft flick, and Lampard quickly added a third on the volley from Mata's cross. Terry headed in at the far post to make it 4-0 on 81 minutes.
In fifth round ties later on Sunday, Manchester City host Championship Leeds United in a 1400 GMT kickoff while second tier Huddersfield entertain Wigan Athletic at 1555.