Manager Brendan Rodgers elected to make eight changes to the XI that beat Chelsea 2-0 in midweek, with Youri Tielemans – captain on the day – James Maddison and Harvey Barnes the three players to remain.
Çağlar Söyüncü and Ricardo Pereira both made their first starts since early December, while goalkeeper Danny Ward made his fourth appearance of the season in all competitions.
Inside the opening three minutes, City twice had a chance to take an early lead, but Ayoze Pérez fired wide before Cengiz Ünder forced Luke Daniels into a comfortable stop at the near post.
However, Brentford's first attack of the game produced an opener, as defender Mads Bech Sørensen stabbed home a flicked-on corner on seven minutes, beating Ward from close range.
City looked for a swift reply, with Pérez and Barnes both having strikes blocked, and then skipper Tielemans drove wide of the target before Maddison curled a free-kick the wrong side of Daniels' right-hand post.
At the other end of the pitch, Ward was on hand to tip Tarique Fosu's effort behind, and then pulled off an excellent save to claw Saman Ghoddos' free-kick out of the top corner, preventing the Bees from doubling their advantage before the interval.
A lightning start to the second period saw City level matters almost immediately, as Maddison wriggled through the Brentford midfield and found, Ünder, whose first-time effort found the bottom corner of the net just 49 seconds after the restart.
Just five minutes later, the Foxes had an opportunity to take the lead when Tielemans was tripped by Fosu in the box, and the Belgium midfielder made no mistake, converting from 12 yards for 2-1.
A superb last-ditch challenge from Ricardo prevented Marcus Forss from restoring parity shortly after, before Ünder had a chance to make it 3-1 to the visitors, but couldn't convert from Ricardo's cross.
But it was City who persisted, looking full of energy as the clock ticked on, and while Barnes was unfortunate to fire wide on 69 minutes, his side's third goal of the afternoon arrived soon after.
It was the Academy graduate who initially had an effort saved by Daniels, but Maddison was there to tuck home the rebound to score his fourth strike in as many games in all competitions, in turn rounding off the win.
Major moment
After a frustrating first half in west London, City started the second period in brilliant fashion, and deservedly drew level through Cengiz Ünder.
Inside the minute, a determined run from James Maddison created an opportunity for the Turkey star, who whipped an effort into the bottom corner to spark the comeback.
A Youri Tielemans penalty, and James Maddison's close-range finish, made sure of the win, but it was Ünder's leveller that gave Leicester hope at the start of the second half.
Who impressed?
Speaking on LCFC Radio, Matt Elliott said: “Cengiz Ünder I thought first half was the biggest threat. We mentioned it at half-time and he got himself a goal. For me, Barnes has done well [in the] second half, but watching it live, the best player on the pitch has been Youri Tielemans. He was the general and he ran the show."
Where do we stand?
The Foxes will face Brighton & Hove Albion in the fifth round at King Power Stadium, with the tie set to take place in the week commencing Monday 8 February. Full fixture details will be confirmed in due course.
Coming up…
City’s Premier League campaign resumes on Wednesday evening when they head to Goodison Park to face Everton (8:15pm kick-off), before a clash with Leeds United at King Power Stadium on Sunday (2pm kick-off).
All times GMT.