Second-half goals from Michael Ballack, Frank Lampard and Deco cancelled out Darren Bent's 18th-minute strike for Sunderland in a match dominated by the visitors.
Chelsea, who also fought back to win 2-1 against Hull City on Saturday, began another rally with a Ballack equaliser seven minutes after the break following a Lampard corner.
The Londoners scored again after 61 minutes when George McCartney's foul on Didier Drogba allowed Lampard to convert a penalty and equal Jimmy Greaves's record as the club's fifth all-time scorer with 132 goals.
A fine strike by Portugal midfielder Deco with 20 minutes remaining sealed the victory.
Elsewhere, promoted Wolverhampton Wanderers held on at Wigan Athletic for their first victory of the season, winning 1-0 courtesy of a sixth-minute header from Andy Keogh.
Wigan, who recorded a 2-0 triumph at Aston Villa on the opening day, pressed hard after the break with on-loan Chelsea winger Scott Sinclair wasting the best chance with a header.