The hosting Blues created the better of the chances during the opening 45 minutes, but Oscar struck the post when he just had Simon Moore to beat, before Frank Lampard failed to find the target from close range just before the break.
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Sandwiched between those efforts, visiting Brentford did manage to put the ball in the net, but Marcello Trotta's strike was ruled out for a foul that had been committed earlier in the move.
Chelsea stepped up the intensity after the restart and went on to score four unanswered goals.
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Their lead was then doubled 12 minutes later as Brazilian midfielder Oscar flicked in a low cross from Branislav Ivanovic from inside the six-yard box.
Rafael Benitez's side continued to attack and they put the game out of Brentford's reach with 72 minutes played. Mata turned creator on this occasion as he sent over a lofted pass for Lampard, who volleyed into the goal to leave him just three away from becoming the club's all-time leading goalscorer.
The scoring was completed in the closing stages by captain John Terry, who rose highest at the back post to head in a deep cross from Oscar with six minutes left to play.
Chelsea will now travel to Middlesbrough for a place in the quarter-finals.