Frank Lampard scored with a brilliant free-kick as Chelsea opened their Champions League campaign with a win.
Lampard's strike swerved viciously and completely deceived Anderlecht keeper Daniel Zitka, who had earlier saved from Michael Essien and Damien Duff.
Zitka saved another Lampard free-kick in the second half, parrying the ball after making a full-length dive.
Anderlecht almost equalised when Anthony Vanden Borre's long-range strike hit the post.
Lampard's goal had seemed the prelude to several more but Chelsea - despite dominating possession and territory - failed to breach the Anderlecht defence again.
And the longer the match went on the more the visitors threatened - making it a nervous finish for the modest crowd of 29,575.
Chelsea boss Jose Mourinho had made several changes from the team that beat Sunderland on Saturday, recalling defender Ricardo Carvalho for his first start of the season.
And the Blues almost opened the scoring after just four minutes, Zitka denying them twice in quick succession.
Zitka covered his near post to parry Essien's shot from a tight angle and seconds later acrobatically tipped Duff's long-range strike over the crossbar.
A threaded ball from Mbo Mpenza underlined the visitor's attacking threat but, after collecting the pass, Akin Serhat sliced his shot wide under pressure from William Gallas.
An Anderlecht corner briefly caused confusion, but Chelsea broke the deadlock shortly afterwards.
Following a short lay-off from Arjen Robben, Lampard smashed the ball past Anderlecht keeper Zitka, who was moving in the wrong direction as the ball swerved and flew past him.
Chelsea passed and probed through the remainder of the opening half, with Gallas drilling a shot wide from distance and Didier Drogba getting close to a couple of teasing crosses.
Anderlecht continued to make life hard for Chelsea after the break, maintaining a well-organised defensive formation.
Zitka improved on his first attempt to save another Lampard free-kick, getting two hands to a well-struck shot that, unlike the goal, did not swerve.
The visitors then reminded Chelsea of the danger of leading by a single goal when Vanden Borre's strike deflected off John Terry and hit a post.
Chelsea substitute Shaun Wright-Phillips shot over from the edge of the box in injury-time, while defender Robert Huth came on as the home team held out for the final whistle.
Chelsea: Cech, Paulo Ferreira, Terry, Ricardo Carvalho, Gallas, Duff (Joe Cole 77), Essien (Huth 90), Makelele, Lampard, Robben (Wright-Phillips 67), Drogba.
Subs Not Used: Cudicini, Crespo, Geremi, Diarra.
Goals: Lampard 19.
Anderlecht: Zitka, Zewlakow (Jestrovic 81), Juhasz, Tihinen, Deschacht, Vanden Borre, Vanderhaeghe (Delorge 89), Deman, Goor, Mpenza, Akin (Wilhelmsson 70).
Subs Not Used: Proto, Baseggio, Hasi, Zetterberg.
Booked: Akin, Vanderhaeghe.
Ref: Wolfgang Stark (Germany).