Anelka could have earned the Blues only their second league win in the last 12 visits to Villa Park but his downward header from Ashley Cole's header bounced up and against the crossbar.
It would have been rough justice on Villa who had done enough to earn at least a share of the spoils - and should themselves have won the game in injury time as Nigel Reo-Coker shot wide when one-on-one with keeper Petr Cech.
So close: Nicolas Anelka almost snatches a win for Chelsea
Villa missed a great chance to open the scoring through Stephen Ireland after three minutes.
Stewart Downing made a good break down the right flank and his low ball picked out the run of Ireland who took the ball in his stride. The former Manchester City player's cross-shot beat the dive of Cech but flew inches wide of the far post.
Villa dominated the early stages and Cech produced a fine save to deny John Carew.
Stephen Warnock won the ball off Ramires and it ricocheted straight into the path of the Norway striker. He cut inside before drilling a low shot which Cech fingertipped around the post.
Paolo Ferreira then made a fine tackle to deny Carew another shooting opportunity after Ashley Young had threaded the ball into his path.
Blown it: Nigel Reo-Coker reflects on his miss
Villa were forced into a substitution after 13 minutes when Richard Dunne did not reappear after going down the tunnel for treatment following a challenge by Ramires.
He was replaced by youngster Ciaran Clark rather than the experienced Carlos Cuellar.
Michael Essien became the first player to be booked for bringing down Villa skipper Stiliyan Petrov.
Villa were soon back on offensive and Petrov had a shot deflected wide after Ireland had teed him up on the edge of the Chelsea box.
Chelsea started to enjoy a fair slice of possession and Mikel had the their first on target attempt after 33 minutes although it was comfortably dealt with by Villa keeper Brad Friedel.
But in a Villa counter-attack Branislav Ivanovic threw his body forward to block a fierce drive from Ireland 20 yards out.
Close run thing: Ciaran Clark watches as his effort beats Petr Cech but bounces off the post
Ancelotti made a half-time switch with the ineffective Kakuta replaced by Yuri Zhirkov.
There was more urgency about the visitors' play in the early part of the second half.
Malouda warmed the palms of Friedel with a powerful 25-yard drive, although he had his body right behind the shot.
Along ball played in Anelka behind the Villa defence and, after he hadcut back inside, his low shot was blocked by the legs of Friedel.
Clark then got a vital touch on a cross from Zhirkov with Anelka unmarked behind him.
Inseperable: Much like Michael Essien and Stephen Ireland, there was little between the two sides at Villa Park
Terrywas yellow-carded after 59 minutes for a heavy challenge on Young andWarnock was booked for a mistimed challenge on Anelka six minutes later.
The bookings were now coming thick and fast and Ireland was cautioned for hauling down Malouda in a Chelsea counter-attack.
Ivanoviccame close to breaking the deadlock after 77 minutes when he poweredhis header against the near post from Malouda's corner.
Butthen the woodwork came to Chelsea's rescue when Young's free-kick hitthe back of Terry's head and then deflected off Clark onto a post.
Net result: Brad Friedel kept another clean sheet as Villa continued their recent good form under Gerard Houllier
Young was yellow-carded for dissent after protesting too much at a free-kick awarded against him for fouling Jose Bosingwa.
Then Chelsea substitute Josh McEachran was booked for a challenge on Habib Beye.
Anelka headed against the bar from Cole's cross in the last minute of normal time.
Then,with almost the last kick, Reo-Coker found himself in space but lackedthe necessary composure and shot wide, ensuring the match endedgoalless.
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