Further goals from Alex and Frank Lampard, his 100th Premier League goal, completed the rout.
Chelsea went back to the top of the league, albeit for a couple of hours, and served a warning to the rest of the Premier League that their home defeat last week to Liverpool was just a blip.
Chelsea's first effort on the Sunderland goal came on three minutes from Florent Malouda, surprisingly shooting from distance with his right foot with the unsurprising result that it went wide of goal.
Four minutes later, Ashley Cole found himself in an advanced position working well with Malouda, but a tussle with Pascal Chimbonda saw the left-back scuff his shot from six yards out.
Malouda forced the first save from Marton Fulop of the match on 15 minutes, diving well to his left. But a minute later he was beaten all ends up when Deco let fly from just outside the visitor's area, only for his right-footer to skim off the crossbar to safety.
But the deserved breakthrough came on 27 minutes when Joe Cole weaved his way through the Sunderland defence and daisy-cutted a left footer.
Fulop could only deflect the ball across goal into the gleeful path of centre-back Alex who coolly slotted home, unmarked from two yards.
Alex then assisted number two, three minutes later. Lampard sent in a low ball on the right. The ball was pushed on by Alex but Anelka, seemingly in an offside position tapped the ball home - again from two yards out.
The first substitution of the match involved Ashley Cole, who was injured in a clash with Steed Malbranque and was replaced by Wayne Bridge on 36 minutes.
The third goal cam on 45 minutes and again it was a tap-in. A quick counter-attack saw Sunderland's rearguard completely humbled as Malouda's pinpoint pass to Anelka, this time, onside, gave the striker the easiest of chance to flick the ball into the empty net.
Roy Keane rang the half-time changes replacing the ineffectual Malbranque and Martyn Waghorn with El-Hadji Diouf and Jordan Henderson, but it made no difference and the Blues took just another five minutes to hit number four.
This time Joe Cole's expertly chipped right byline cross was met powerfully by Lampard's header.
It got worse for Sunderland two minutes later when Anelka notched his hat-trick goal sliding in from eight yards out to meet Malouda's left byline cross. Sadly for Fulop, his despairing dive only helped he ball over the line.
Djibril Cisse came on for Kenwyne Jones in the 58th minute with the job of hitting six goals while Chelsea withdrew Joe Cole for Didier Drogba five minutes later.
Sunderland finally got into Chelsea's area on 67 minutes but Petr Cech palmed the ball out of the way of the advancing Cisse and the attack petered out.
Carlos Mineiro, an out-of-contract player from Hertha Berlin, made his Chelsea debut for Anelka on 75 minutes as Chelsea ran down the clock and gained three valuable points.