Thomas Frank's men were given the perfect start by Mads Bech Sørensen who reacted quickest from a corner to score. The Foxes managed to turn the game around though at the start of the second half, with a Cengiz Under finish and a Youri Tielemans penalty seeing the Premier League side take the lead.
James Maddison rubber-stamped the victory with 20 minutes remaining, tapping in after Luke Daniels failed to hold a low effort from Harvey Barnes. They will now meet top flight rivals Brighton and Hove Albion in the fifth round of the competition.
Story of the Match
Bees control opening half
Despite enjoying much of the ball in the early stages with chances from Ayoze Perez and Under, Leicester found themselves behind within seven minutes. From a corner that was sloppily given away, the ball ricocheted off of Daniel Amartey and Nampalys Mendy before falling to Sorensen, who stabbed in from close range.
The hosts might well have doubled their lead from another corner, with the ball falling to Tariq Fosu at the back post but his volley was palmed behind by Leicester stopper Danny Ward. The Foxes goalkeeper was then called on again to paw away Saman Ghoddos' free-kick that looked to be arrowing towards the top corner.
Leicester recover after the break
Whilst Brentford looked the most likely to add to their lead before the break, it was a much-improved Leicester performance after half-time, with the Foxes managing to stage an impressive turnaround. Almost instantly after the restart, Maddison managed to feed the ball to Under who tucked past Daniels with a cool left-footed finish.
It then got worse for the home side as Fosu attempted to dispossess Tielemans in the penalty area but only served to bring down the Belgian, with the referee awarding a spot kick. It was the midfielder who stepped up and scored with a cool finish into the bottom-left corner.
Maddison books fifth round ticket
Now in their groove, Leicester looked ominous and Under almost added to his afternoon's work but fired an effort wide of the far post.
Maddison ensured that the visitors did get their third. Barnes at first swaggered into the penalty area to test Daniels with a low effort, with the ball then falling to Maddison just yards out. He had an easy task, tucking home unchallenged to book Leicester's progression.
Set pieces trouble Leicester again
Rodgers' Foxes have become infamous with their inability to defend set pieces in the Premier League this season having already conceded eight throughout the season. That problem troubled them again against Brentford with the hosts claiming their opening goal from a corner. It goes without saying then that Leicester really need to fix that aspect having seen it plague their campaign thus far.
Tucking away Leicester's third goal, Maddison extended his brilliant recent form. The midfielder has now scored in his last four appearances in all competitions, the first time he has managed that in his Leicester career. Also notching an assist for Leicester's equaliser via Under, it now means he has nine goals and seven assists in all competitions already in 2020/21, just one below his best goal contributions count for the Foxes.
Just one too far for Brentford
Coming into the match, Brentford were always going to be a tough opponent for the Foxes having already beaten Southampton, West Bromwich Albion, Fulham and Newcastle United in the Carabao Cup. Despite giving Leicester plenty to think about before half-time, they just weren't quite able to sustain their performance and fell to what was eventually an admirable defeat. They will now instead focus on their battle for promotion from the Championship.