After a season of shocks, the upsets dried up in the fifth round as Birmingham City came from behind to win 2-1 at Championship side Derby County with a last-minute goal by Liam Ridgewell while Manchester City and Stoke City drew 1-1.
Reading, conquerors of Liverpool and Burnley in previous rounds, drew 2-2 at home to West Bromwich Albion after taking the lead after nine seconds of the all-Championship tie.
Saturday's game at Stamford Bridge was preceded by a minute's applause in honour of former Chelsea and Yugoslavia goalkeeper Petar Borota after he died at the age of 57.
"They played exceptionally well in the first half but fortunately we upped the tempo in the second and in the end it was easy for us," Chelsea assistant manager Ray Wilkins told reporters.
However, as so often this season, Roberto Mancini's team failed to push on and Stoke levelled after 57 minutes when Ricardo Fuller headed in a Rory Delap long throw.
Rickie Lambert equalised but Aruna Dindane, Nadir Belhadj and Jamie O'Hara completed a rare win for the visitors.
Jimmy Kebe's goal for Reading was timed by his own club at nine seconds. Others clocked it at seven seconds, either way it beat the previous quickest in the competition proper of 13 seconds by Aston Villa's George Edwards against Manchester United in 1948.
