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Midfielder Frank Lampard scored his 199th goal for Chelsea, who put four second-half goals past Brentford at Stamford Bridge to secure a fifth-round clash at Championship (second division) Middlesbrough on Feb. 27.
Argentine Sergio Aguero scored twice for 2011 winners Manchester City, who eased into the quarter-finals with a confident display that was the complete opposite from their abject surrender in a 3-1 Premier League defeat at Southampton last weekend.
"I think it was really important to win this game. If you score two goals within the first 20 minutes it is easier, but the FA Cup is a difficult competition as Arsenal and Everton showed yesterday," City manager Roberto Mancini told ESPN.
Top-flight strugglers Wigan Athletic put their relegation fears to one side by breezing past second-tier Huddersfield Town 4-1 with two goals from Ivorian Arouna Kone.
Three Championship teams reached the last eight on Saturday, including Blackburn Rovers who stunned 10-times winners Arsenal with a 1-0 victory at the Emirates.
Everton, sixth in the Premier League, were taken to a replay after conceding a stoppage-time goal in a 2-2 draw at third-tier strugglers Oldham Athletic.
England midfielder Lampard, whose Chelsea future remains unresolved with his contract expiring at the end of the season, tucked away a simple volley on 71 minutes to edge closer to Bobby Tambling's all-time club record of 202 goals.
The goal prompted Chelsea fans to chant "sign him up" as billionaire owner Roman Abramovich, sat with hands deep in his pockets, forced a wry smile high up in the stand.
Interim manager Rafael Benitez said: "The team was doing well and Frank Lampard is scoring goals, which is good for him and good for us."
Chelsea twice had to come from behind to earn a 2-2 away draw in their first encounter and were again sluggish in the first half against their fellow Londoners.
Juan Mata finally broke Brentford's resistance on 54 minutes when he latched on to Demba Ba's flick from a long Petr Cech clearance and drilled in a left-foot shot from 20 metres.
Oscar doubled the lead 14 minutes later from Branislav Ivanovic's cutback, scoring with a deft flick, and Lampard quickly added a third from Mata's cross. John Terry headed in at the far post, this time from Oscar's curling delivery, to make it 4-0 on 81 minutes.
"First half they made it very difficult, they sat very deep. Once we got the first goal, the second and third were sure to come," Terry, returning after missing two matches with an inflamed knee, told ITV.
Terry said a British newspaper report on Sunday that he and Benitez were involved in a dressing room bust-up were "complete rubbish".
"There are stories today in the paper but it is complete lazy journalism," the defender said, referring to a Sun newspaper story headlined "War".
With his side 12 points behind Manchester United and their Premier League title hopes fading, Mancini had demanded his players atone for the Southampton loss which he had described as City's worst game in the last two or three years.
City duly obliged, crafting a brilliant opener after five minutes that was started and finished by Yaya Toure.
The Ivorian exchanged passes with David Silva and Carlos Tevez before slotting home and Aguero doubled the lead on 14 minutes from the penalty spot.
Tevez bundled in a third after 52 and Aguero rifled in the fourth 16 minutes from time.