Second-half goals overnight from Willian, Gary Cahill, Eden Hazard and Bertrand Traore at Stamford Bridge sent the Blues into the quarter-finals.
With a Champions League trip to Dynamo Kiev on Wednesday and the League Cup final against Liverpool next Sunday, Manchester City manager Manuel Pellegrini started six teenagers, five of whom were making their first-team debuts.
The youngsters were level at the half as debutant David Faupala canceled out Diego Costa’s opener.
Chelsea’s experience eventually came through with Willian and Cahill scoring in the opening eight minutes after the restart.
Hazard made it 4-1 and, after Oscar had a penalty saved, Bertrand Traore completed the scoring.
Crystal Palace produced the upset of the day by beating Tottenham 1-0 to reach the quarter-finals for the first time in 21 years.
Martin Kelly scored his first goal in over four years as Palace beat a third straight Premier League foe and avenged two league losses to Spurs.
“We had some great performances out there,” manager Alan Pardew said.
“We learnt our lessons from two previous meetings with Spurs.
“It was a victory that was well earned on the training ground.” Tottenham came up empty on 19 shot attempts as Dele Alli hit the post and Palace keeper Wayne Hennessey twice saved from Harry Kane.
“It like a Premier League game but you need to be clinical in front of goal,” manager Mauricio Pochettino said.
“We managed the game, created chances but it was difficult to win.” West Ham rolled over Blackburn Rovers 5-1 as Dimitri Payet and Emmanuel Emenike scored twice each.
Victor Moses also scored for West Ham after Ben Sheppard gave Championship side Blackburn an early lead.
“After the first 20 minutes we played fantastic,” Hammers manager Slaven Bilic told BT Sport. “We really played great football.
“It looked easy but it’s not as easy, we know that.
“We made it look easier than we thought. But only because our performance was really spot on.” Both teams finished with 10 men after Blackburn’s Chris Taylor was shown a second yellow card and West Ham’s Cheikhou Kouyate saw straight red for a foul as the last man back.
“I thought for 55 minutes we were very good and well in the game,” Blackburn manager Paul Lambert told the BBC.
“The sending off kills us. It’s hard enough against 11 let alone 10.”
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