Steven Fletcher's double and Jordi Gomez's strike have lifted Gus Poyet's men out of the drop zone, while Neil Warnock's side have suffered their third loss in four games
The 27-year-old put Gus Poyet’s men in front after 31 minutes before an own goal from Wes Brown levelled the score in the second half.
Jordi Gomez struck with 11 minutes remaining, while Fletcher netted his second of the game in injury time to lift Sunderland out of the relegation zone and end the club's run of back-to-back defeats.
Palace, who had Mile Jedinak sent off late on, have now suffered their third loss in four games.
Poyet dropped goalkeeper Vito Mannone following his error against Arsenal last weekend, with Costel Pantilimon making his first Premier League start for Sunderland since his arrival from Manchester City. Anthony Reveillere, signed on a free transfer last month, was also handed his Sunderland debut.
Scott Dann returned to the Palace starting line-up after recovering from a knee injury, with Adrian Mariappa dropping to the bench in the only change to the side that drew at West Brom.
Neil Warnock felt Palace were on the wrong end of poor decisions from officials in their last two games and he was entitled to feel aggrieved again when referee Phil Dowd failed to award a penalty inside 30 seconds.
Santiago Vergini appeared to upend Fraizer Campbell after the former Sunderland striker outpaced him to race onto a Marouane Chamakh flick, but Dowd waved play on.
The hosts showed plenty of endeavour, but lacked quality in the final third and it was Sunderland who were in front with a goal against the run of play after 31 minutes.
Palace were caught out when Fletcher rose to guide a fine header inside Julian Speroni's right-hand post after he was picked out by Patrick van Aanholt.
The home side had another penalty shout when Wilfried Zaha went down under a challenge from Van Aanholt soon after going behind, but Dowd again saw nothing untoward.
Van Aanholt was carried off due to a shoulder injury sustained in that incident, with Brown replacing him.
Fletcher tested Speroni with a right-footed strike and Vergini was denied by the Palace goalkeeper in first-half stoppage time as Sunderland grew in confidence after going in front.
Palace made a bright start to the second half and they were level nine minutes after the break courtesy of Brown.
Zaha stood a ball up to the back post for an unmarked Chamakh and, although Pantilimon somehow kept out the striker's close-range header, the keeper was unable to prevent Brown from finding the back of his own net after Campbell had back-heeled the ball into his path.
Sunderland responded and Gomez fired home from 20 yards out to restore the visitors' lead in the 79th minute, then Jedinak was shown a second yellow card four minutes from time after appearing to kick out at Gomez.
Fletcher added his side's third in time added on with a neat right-foot finish to add insult to injury for Palace.