The Blues took the lead with a touch of fortune and a sense of deja vu in the 25th minute.
It was not quite a carbon copy of Fernando Torres' late winner against Manchester City on Sunday but it was certainly close as a high, looping ball caused confusion in the Arsenal defence and the unlikely figure of Cesar Azpilicueta ran through to get a toe on Carl Jenkinson's poor header towards Lukasz Fabianski.
There was nothing lucky about the second, however, as Juan Mata showed some fine skill, controlling with his left before lashing home a right-footed shot.
Manchester United join Chelsea in the quarter-finals after dispatching Norwich 4-0 with Javier Hernandez scoring twice to strengthen his claims for more regular playing time.
The Mexican got his first from the penalty spot in the 20th minute after Leroy Fer somewhat needlessly felled Adnan Januzaj, and then headed in a second on the rebound early in the second half after Mark Bunn could only parry his initial effort.
Phil Jones then volleyed in a third but by then, Norwich were more concerned by the condition of Robert Snodgrass, taken off on a stretcher wearing a neckbrace, after a lengthy stoppage which followed a clash of heads.
The incident led to 11 minutes of added time being played, and United used them to add a fourth through substitute Fabio.
Fulham's patchy Premier League form carried over to the cup as they were knocked out by Leicester in a 4-3 thriller at the King Power Stadium.
Hugo Rodallega capitalised on some poor defending to give the away side an 18th-minute lead, but Leicester scored three in quick succession either side of half-time to turn it around.
Wes Morgan levelled in the 41st minute on the rebound after Maarten Stekelenburg failed to hold Anthony Knockaert's free-kick, and Chris Wood put the Foxes ahead just before half-time when Philippe Senderos's clearance was blocked and the ball fell kindly.
Miguel Ignasi headed in a third early in the second half before Rodallega's almost instant response for Fulham set up a late rally, which looked complete when Giorgos Karagounis fired in an 86th-minute free-kick.
But no sooner were they level than Lloyd Dyer struck what would prove the winner.
West Ham edged out Sky Bet Championship leaders Burnley 2-0 at Turf Moor with both goals coming from the penalty spot late on.
Matthew Taylor got the first in the 76th minute after Jason Shackell brought down Kevin Nolan while Jack Collison tucked away the second in stoppage time after being fouled by Keith Treacy, who saw red to complete Burnley's misery.