The Brazilian opened the deadlock with a 35-yard effort before John Terry scored a goal in each half as Chelsea showed defenders were the best form of attack against the Cottagers.
The home side showed plenty of nice touches in the game but the quality came from the Blues and the three points over their west London rivals takes them above Arsenal into third.
Bryan Ruiz could have opened the scoring inside three minutes when he almost latched onto a Sascha Riether cross, while Giorgos Karagounis also fizzed a shot just over the bar early on.
But just as Rafael Benitez's side seemed to be in passive mood, Luiz stepped out from the back on the half-hour mark to unleash an outrageous strike that had Mark Schwarzer grasping at thin air.
The goal did little to change the pattern of play with Fulham enjoying considerable possession as Petr Cech saved well from Urby Emanuelson before Dimitar Berbatov drilled just wide of the post.
But Chelsea were the more clinical side and Frank Lampard - restored to the team with Terry after both were left out of the FA Cup semi-final - soon troubled Schwarzer with a powerful free-kick.
From the resultant corner, Juan Mata looped a cross in from the right and Terry did well to pull away onto Philippe Senderos and climb above his opponent to head in at Schwarzer's near post.
That saw Chelsea go in two-goals up at the interval and while Martin Jol's side tried to find a second-half response, with Mladen Petric spurning two chances, the third goal killed the game off.
With 20 minutes to play, Fernando Torres flicked a corner on at the near post and Terry was there ahead of Riether to force the ball over the line and grab his second goal of the game.
This time there was no reaction from Fulham and Benitez was even able to withdraw some of his overworked players as they aim to build on this comfortable victory and secure a top-four spot.