Anelka's 21st goal of the season sent Villa spinning to defeat in a pulsating match which was marked by the different styles of the two teams.
It was also an occasion of firsts. It was Chelsea's first league success at Villa Park in ten years, while it was Martin O'Neill's side's first league defeat in 14 games, as they were denied a share of the spoils by a brilliant display of goalkeeping from Petr Cech.
Chelsea's new manager, Guus Hiddink, marked his first game in charge with a victory as the Blues revealed some vintage form in an attempt to revive a season which had been flagging until this impressive win.
Just as important Chelsea chalked up an impressive double over a Villa side who appear to be struggling a little under the pressure of a heavy match programme, which continues in Moscow against CSKA next Thursday.
Looking for revenge for the 2-0 defeat at Stamford Bridge last October when Chelsea were the only team to have outplayed Villa this season, the Midlands club finished the game peppering the opposition, but the Londoners held on for a vital win.
The visitors made the more positive start than Villa, with Didier Drogba and Frank Lampard both producing good goal attempts in an attempt to quieten the home fans.
Villa, however, bounced back with several raids down the middle but it was significant that the service to Ashley Young had been cut off, forcing the young England winger to move across to the right to get into the game.
Chelsea, all in black, did not treat the game as a sombre occasion. Far from it, they delighted the capacity crowd with some delightful football which was brilliantly highlighted when the Londoners went ahead in the 19th minute.
Lampard, driving forward, brilliantly side-stepped a couple of Villa defenders to put Anelka in possession and the French striker lifted a shot over Brad Friedel for his first league goal in nine games.
The goal lifted Chelsea to an even higher plain as they mounted even stronger pressure on the over-worked Villa defence, as if the Londoners were determined to make up for their recent indifferent results and in the process impress their new manager.
This invigorating approach was emphasised in a hectic assault on the Villa goal when Salomon Kalou was denied a goal by a desperate late tackle, before John Terry's header from the resulting corner was brilliantly saved by Friedel.
Villa's response was a free-kick from Ashley Young which cannoned off the crossbar with Petr Cech nowhere near the ball.
It was significant that in a first half dominated for long spells by Chelsea that Villa's skipper, Gareth Barry, struggled to make an impression as he was over-shadowed by the brilliance of Lampard and Barrack.
One player who appeared intent on getting his name on the scoresheet was Terry. Only a goal-line clearance by Stiliyan Petrov prevented the Blues skipper from netting with a powerful header.
In an action packed encounter Gabriel Agbonlahor gained possession following a slip by Alex. The England striker found himself with only Cech to beat, but the goalkeeper narrowed the angle on the near post and made a smart save.
The Czech international keeper again excelled when he parried a point-blank shot from Barry as Villa were thwarted from grabbing an equaliser.
Barry was later denied again by Cech, which appeared to cap a frustrating game for Villa.