Didier Drogba put Chelsea in front in the second minute but Michael Chopra stunned the home side with an equaliser before the interval.
Chelsea were back in front in the 51st minute when Drogba's pass evaded Mark Kennedy to put Michael Ballack through on goal. The Germany captain kept his cool to volley the ball over David Marshall and make it 2-1.
Chelsea then wrapped up the game as goals from Daniel Sturridge and substitute Salomon Kalou put Carlo Ancelotti's side into the last eight.
Portsmouth were in danger of being put out of business this week but they are alive in the FA Cup after defeating rivals Southampton 4-1 at Fratton Park.
Despite being matched by Alan Pardew's men for much of the fifth-round clash, Quincy Owusu-Abeyie came off the bench and opened the scoring for the visitors at St Mary's.
Rickie Lambert levelled shortly after but Aruna Dindane, Nadir Belhadj and Jamie O'Hara netted to give the scoreline a flattering look for the bottom club in the Premier League.
Jimmy Kebe scored the fastest goal in the FA Cup proper when he put Reading ahead against West Brom after just nine seconds. Kebe slotted a left-footed shot into the net to stun the Baggies straight from the kick-off and although Gareth Morris scored after four seconds for Ashton United in 2001, that came in the qualifying rounds, meaning the Royals midfielder made his own piece of history.
However, West Brom drew level in the 18th minute through a well-worked goal, Robert Koren converting Chris Brunt's cross from the right.
Reading went ahead again after the break as Simon Church slotted home in the 73rd minute, but Joe Mattock forced a replay with just three minutes left as he drilled a low shot past Adam Federici to end the game 2-2.
Nigel Clough's dream of winning the one domestic trophy which eluded his father, Brian, was shattered as Birmingham defender Liam Ridgewell snatched an injury-time winner in the FA Cup fifth round tie to beat Derby 2-1 at Pride Park.
Jay McEveley's 54th minute strike put the Rams on course for a quarter-final spot for the first time in 11 years although Blues keeper Joe Hart will shoulder some of the blame. But Scott Dann headed home a James McFadden corner to level matters and then Ridgewell popped up with the decider after a rebound from Kevin Phillips' shot.
