The Black Cats hit the front in just the fourth minute through Phil Bardsley before the Blues rallied, scoring twice before the 25-minute mark through Frank Lampard from the penalty spot and then Samolon Kalou with a neat finish.
Sunderland were able to hit back when Kieran Richardson guided in his 27th minute free-kick but that only got Chelsea going as they dominated the second half, taking the lead through skipper John Terry on the hour-mark before Nicolas Anelka wrapped it up in injury time.
The win sees Ancelottiâ€™s men cut Manchester Cityâ€™s lead over them to just one point with their third league win on the trot as Sunderland, who were gallant in defeat, remained sixth on the table despite their first loss in five league games.
GOAL Sunderland were hoping they could back up their 3-0 away win over Chelsea at Stamford Bridge in November and it started perfectly when Phil Bardsley fired home from the edge of the area past an unsighted Petr Cech.
After the goal, the Blues looked decidedly more dangerous by picking up the running and it worked in their favour when Black Cats defender Ahmed Elmohamady brought down Ashley Cole in the area with a clumsy challenge, forcing referee Mark Halsey to point to the spot.
GOAL Frank Lampard stepped up to the plate and sent Craig Gordon the other way to restore parity.
In a very open affair, both sides were attacking at will and there was soon a third goal inside 25 minutes.
GOAL Chelsea hit Sunderland on the break where Nicolas Anelka played a neat ball into the path of Salomon Kalou who beat an advancing Gordon by chipping it beyond the home keeper to make it 2-1.
GOAL Less than three minutes later, the Black Cats were on level terms with a fourth goal of the match in the opening half-hour. Elmohamaday won a free-kick for his side with Kieran Richardson sending a dead ball past the wall which then evaded Cech, giving the home side more hope.
Sunderland were extremely when two strong Chelsea chances went the home sideâ€™s way. The first one was from a strong Michael Essien shot which Gordon denied in the 37th minute before Branislav Ivanovic hit the crossbar from six yards out moments later.
Gordon was well-placed when Didier Drogba tried his luck with a 40th minute header before Richardson caused some more uncertainty for Cech with a rasping shot down the other end but the Blues gloveman was able to parry away in what was the last chance of any note for a scintillating opening half.
Chelsea had a couple of good chances in the fourth minute of the second term when Gordon was able to scuttle away a Lampard effort before Steed Malbranque and the post kept out the ensuing corner. Lampard was then again denied by Gordon as the Blues were unlucky not to be ahead.
GOAL The visitors then got a deserved goal in the 60th minute when Lampard was yet again denied by Gordon but John Terry was on hand to somehow loop a shot over the Black Cats keeper to make it 3-2.
It should have been 4-2 about four minutes later when Kalouâ€™s shot hit both posts but failed to get over the line with the Blues looking very, very dangerous although Sunderland debutant Stephane Sessegnon forced Cech into a vital save in the 70th minute.
A little bit of a fracas occurred with just under 10 minutes left when Richardson and Ivanovic clashed, attracting a few players in the one area, but it was the Black Cats man who was booked for kicking the ball at Jose Bosingwa in frustration.
GOAL But the Blues werenâ€™t done and managed a fourth in injury time when substitute Florent Malouda did some nice work before setting up fellow Frenchman Nicolas Anelka for an easy finish.
Craig Gordon (gk), Titus Bramble, Phil Bardsley, Nedum Onuoha (Cook 85â€™), Anton Ferdinand, Steed Malbranque (Colback 80â€™), Kieran Richardson, Stephane Sessegnon, Jordan Henderson, Ahmed Elmohamady, Asamoah Gyan
Petr Cech (gk), Ashley Cole, John Terry, Branislav Ivanovic, Jose Bosingwa (Ferreira 90â€™), Frank Lampard, Michael Essien, John Obi Mikel (Ramires 77â€™), Didier Drogba, Samolon Kalou (Malouda 82â€™), Nicolas Anelka