The hosts looked the better of the two sides early on, but David Luiz’s devastating long-range strike and John Terry’s easy header gave the Blues a two-goal lead at the break and the visitors never looked back, with the Chelsea skipper adding a second header to kill the game off.
Rafael Benitez made four changes from the FA Cup defeat to Manchester City, bringing Terry and Frank Lampard back in, with Victor Moses preferred to Oscar and Fernando Torres getting the nod ahead of Demba Ba.
The Blues boss was hoping for a brighter start from his side than Sunday’s semifinal, but the hosts had the better of the opening exchanges, and nearly took an early lead when Sascha Riether swung in a superb cross from the right, but Bryan Ruiz scooped his effort way over the bar from just a few yards out.
Lampard, making his 600th Blues appearance, volleyed straight at Schwarzer before Branislav Ivanovic escaped with a booking for a strong two-footed lunge on Petric.
Giorgos Karagounis fired over and John Arne Riise shot straight at Petr Cech as the hosts looked the better side, but it was Chelsea which took the lead on half an hour thanks to a world-class goal from Luiz, who picked the ball up in midfield before unleashing an absolutely stunning 35-yard strike which swerved into the top corner.
A swerving Lampard free kick was then forced behind by Schwarzer and the resulting corner was cleared, but it came to Juan Mata. The Spaniard swung in a superb cross from the right, and Terry rose unchallenged at the far post to head low into the net and double Chelsea’s lead.
After the break it was again Fulham which started the better of the two sides, enjoying more of the ball, but Chelsea pressed well and stifled any probes forward from the host.
The pace had slowed right down, but a Karagounis corner almost gave Fulham hope as Philippe Senderos produced an unmarked header which was bound for the far corner with Cech helpless, only to see it deflect off Petric and over the bar.
Chelsea immediately punished the Cottagers as Schwarzer turned a low Moses effort around the post. From the ensuing corner Terry bundled Torres’ flicked header into the net from close range for his second of the night.
With the result beyond doubt Chelsea relaxed, allowing Fulham plenty of the ball, but the Cottagers couldn't find their way through an organized defense and the Blues saw out the closing stages of the game to pick up a comfortable three points.