Phil Bardsley’s early long-range effort gave the home side the lead before Frank Lampard equalised from the spot 10 minutes later.
Anelka, who was instrumental throughout showing great poise and awareness on the ball, then created Salomon Kalou’s first-half goal with a sublimely weighted pass but Kieron Richardson equalised for Steve Bruce’s side just three minutes later.
Captain John Terry then put the visitors ahead on the hour-mark and Anelka then sealed the match deep into added time with a deft finish past Sunderland goalkeeper Craig Gordon.
The match began at a frenetic pace and just four minutes in former Manchester United right-back Phil Bardsley was afforded time and space on the right wing before he jinxed past the stationary Jon Obi Mikel and rifled a low shot past Petr Ã„Å’ech in the Chelsea goal.
It sparked an immediate reaction from the reigning Premier League champions. John Terry had a penalty claim denied by referee Mark Halsey and Frank Lampard flashed a shot wide of Gordon’s goal moments later.
Terry, who was frustrated by Halsey’s denial of a spot-kick, was appeased when Ahmed Al-Muhammadi’s clumsy challenge on Ashley Cole resulted in a chance for Lampard to equalise from the spot.
The 32-year-old confidently dispatched the penalty to level matters but the match continued as an end-to-end affair and the fans were afforded little time to gather breath before Kalou’s strike propelled Chelsea into a 2-1 lead after a frenzied 22 minutes.
In seasons past the Blues may have taken control of proceedings and ground out a victory but a clumsy foul by Branislav IvanoviÃ„â€¡ on the edge of Ã„Å’ech’s area just four minutes later resulted in a promising set-piece opportunity for Sunderland.
Richardson then ingeniously whipped a low shot under the feet of the jumping Chelsea players in the wall and past the motionless Ã„Å’ech.
Sunderland managed to contain their opponents for the remainder of a whirlwind first-half largely thanks to the acrobatics of Gordon, who saved efforts from both Michael Essien and Didier Drogba.
Such was the urgency of Chelsea’s play after the interval that it was Terry who often provided support to the visitor’s attacking moves.
Chelsea began to look increasingly threatening from set pieces and a 48th-minute corner almost resulted in a third for the away side with Gordon making a last-ditch save at the feet of Kalou.
And Minutes later Anelka’s darting run and perfectly timed pass to Terry was palmed wide by the Sunderland goalkeeper but from the ensuing corner the Chelsea captain smashed a left-footed drive into the roof of the net.
Ancelotti’s men showed maturity following their third goal with Sunderland allowed possession but ultimately reduced to tame long-range efforts. Anelka looked dangerous on the counter-attack and his timely run almost resulted in fourth. The French international unselfishly slotted Kalou through on goal but the forward was denied by the woodwork as his shot struck both posts.
Deep into injury time Anelka was rewarded for an industrious performance, a display which reminded Ancelotti that new signing Fernando Torres won’t be an automatic choice if the Frenchman remains in such prolific form.
Substitute Florent Malouda broke to the by-line and crossed to Anelka, who produced a delicate finish to seal three points.
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