Liverpool edged closer to the Champions League knockout stages thanks to goals from Fernando Morientes, Luis Garcia and Djibril Cisse.
Morientes scored with a powerful shot on 34 minutes after chesting down Steven Gerrard's astute pass.
Garcia's goal came just past the hour when he flicked a header from some distance past Silvio Proto.
Anderlecht went down to 10 men after substitute Nenad Jestrovic was sent off, before Cisse wrapped up the win.
With Chelsea losing to Real Betis, Liverpool need just a point from their final two Group G games to ensure they reach the last 16, with a home match against Betis and an away fixture at Chelsea still to come.
Liverpool manager Rafael Benitez had opted to field Morientes together with Peter Crouch in attack, two strikers who have struggled for goals this season, with Cisse consigned to the bench.
During the current campaign Morientes has managed to find the net just twice, both those goals coming against CSKA Sofia in the third qualifying round back in August.
Crouch, playing his 13th game on Tuesday, has still to score for Liverpool, and with his luck showing no sign of changing he was eventually replaced by Cisse.
Initially Liverpool's chances fell to Crouch, the lanky striker going close with a couple of headers and a close range shot.
In those early exchanges Morientes was a largely peripheral figure but on the half-hour he moved centre stage, drawing a point-blank save from Proto.
Crouch pounced on the rebound but he was unable to find the net with his shot.
Soon after Morientes drifted out wide and was picked out by Gerrard's chipped pass.
The former Real Madrid striker quickly brought the ball down on his chest before firing a swerving shot past Proto into the corner of the net.
Before Morientes' goal Anderlecht had occasionally troubled Liverpool, notably when Bart Goor went close with a free-kick.
Christian Wilhelmsson's strong running had also caused Liverpool problems.
At the start of second half Liverpool won a succession of corners, Mohamed Sissoko lashing a shot over the bar from one and Jamie Carragher getting in a header from another set piece.
On 51 minutes Benitez withdrew Morientes, replacing the Spanish striker with Boudewijn Zenden.
Ten minutes later Garcia extended Liverpool's lead with a superb header, his looping flicked effort dipping over Proto.
With a quarter of an hour to go Anderlecht's task became even harder when Jestrovic was red-carded by David Beckham's bete noire referee Kim Milton Nielsen.
With two minutes left Cisse showed Crouch how to put the ball in the net, slipping the ball under Proto after having been freed by Harry Kewell.
Liverpool: Reina, Finnan, Carragher, Hyypia, Riise, Gerrard (Kewell 78), Alonso, Sissoko, Luis Garcia, Morientes (Zenden 52), Crouch (Cisse 72).
Subs Not Used: Dudek, Hamann, Josemi, Warnock.
Goals: Morientes 34, Luis Garcia 61, Cisse 89.
Anderlecht: Proto, Zewlakow, Juhasz, Tihinen, Wilhelmsson, Vanderhaeghe (Pujol 70), Deman, Goor, Akin (Jestrovic 70), Zetterberg, Mpenza (Baseggio 82).
Subs Not Used: Zitka, Deschacht, Hasi, Traore.
Sent Off: Jestrovic (75).
Ref: Kim Milton Nielsen (Denmark).