Having lost to Jose Mourinho's Blues in a league encounter at the Etihad 12 days ago, City came out on top this time out as last year's beaten finalists thoroughly deserved their 2-0 victory.
Things started well for the hosts as Stevan Jovetic scored his fourth goal of the season after 16 minutes to put Manuel Pellegrini's side in charge of the tie.
Samir Nasri exchanged passes with David Silva to add the second just six minutes after coming on as a substitute, although Silva appeared to be just offside.
Joleon Lescott turned home a third but was correctly flagged offside as Chelsea failed to truly test Costel Pantilimon over the course of 90 minutes.
Elsewhere, holders Wigan remained in the hunt for this year's competition after winning 2-1 away at Premier League strugglers Cardiff.
Having already seen off top-flight opposition in round four when Crystal Palace were beaten at the DW Stadium, Uwe Rosler's side will now be in the draw for the last eight following a deserved victory in south Wales.
Chris McCann put the Latics ahead in the first half with a cool finish from Jordi Gomez's cross, with Fraizer Campbell levelling before the half hour mark after good work from Magnus Wolff Eikrem.
But it was left to Ben Watson, the man who scored the only goal in last season's final victory over Manchester City, to settle the tie as he thrashed home a winner before the break.
Sunderland continued their transition into a fine cup team as Craig Gardner's stunning finish proved to be the difference as they saw off fellow Premier League side Southampton 1-0 at the Stadium of Light.
Both sides made several changes and the quality of the game suffered as a result but Gardner's strike four minutes into the second half was enough for Capital One Cup finalists Sunderland to advance.
England striker Rickie Lambert missed a fantastic opportunity to take the tie to a replay as Mauricio Pochettino's side bowed out of the competition.
Sheffield Wednesday's fifth-round tie with Charlton was postponed due to a waterlogged pitch at Hillsborough, with both Sky Bet Championship sides going into the draw for the quarter-finals.
Sunday February 16
FA Cup
13:30 Everton v Swansea City
15:00 Sheffield United v N Forest
16:00 Arsenal v Liverpool
Monday February 17
FA Cup
19:45 Brighton v Hull City
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