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 cross 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.
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.
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.
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.
A long ball played in Anelka behind the Villa defence and, after he had cut 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.
Terry was yellow-carded after 59 minutes for a heavy challenge on Young and Warnock 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.
Ivanovic came close to breaking the deadlock after 77 minutes when he powered his header against the near post from Malouda's corner.
But then the woodwork came to Chelsea's rescue when Young's free-kick hit the back of Terry's head and then deflected off Clark onto a post.
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 lacked the necessary composure and shot wide, ensuring the match ended goalless.
Source: Team Talk