Two goals in the opening 15 minutes effectively ended the game as a contest as the Belgian side extended their losing streak in the group stages of the competition to 12 games.
But it could have been very different if the hosts had taken an early presentable chance.
In the seventh minute Christian Wilhelmsson cut the ball back to Mbo Mpenza who wasted the opportunity.
Chelsea moved swiftly to the other end, and when Frank Lampard crossed the ball into the centre, Hernan Crespo was on hand to volley home.
The brittle Anderlecht side were rocked and their heads visibly went down. Just eight minutes later their cause was not helped when Chelsea added a second goal. Crespo headed on a corner and Ricardo Carvalho crashed the ball into the roof of the net.
With the crowd on their backs, it would have been easy for Anderlecht to throw in the towel but to their credit they hit back and when Wilhelmsson found Yves Vanderhaeghe midway through the first half John Terry was forced to block the shot.
Just after the half-hour Crespo fired high and wide before Joe Cole's effort almost caught out Aliaj Sylvio Proto in the Anderlecht goal.
Just before the break Petr Cech was called into action to keep out Bart Goor's deflected shot but it was the Blues that ended the first half in control.
The Belgian side started the second half brightly but it was Chelsea that almost extended their advantage in the 52nd minute when Damien Duff's shot from the edge of the penalty area was parried by Proto.
Anderlecht continued to have their fair share of possession but they struggled to create many clear-cut opportunities, and when Lampard made room for himself with 15 minutes left, Proto was forced to save his shot.
Ten minutes later the England international went closer to scoring when Proto tipped his shot on to the post before Crespo fired just wide.
But Chelsea had done enough to wipe away the memory of their 1-0 defeat at Real Betis last time out as they joined Liverpool and Arsenal in the last 16 of the Champions League with one group game, against Rafa Benitez's side, still to play.