The Black Cats opened the scoring in the ninth minute through Lamine Kone before three goals in the last few minutes of the first half put them out of reach against their fellow strugglers.
The deadlock was surprisingly broken when the Swede sent a free kick into the path of Kone, who headed goalwards, and despite Wayne Hennessey's save under pressure, the Ivory Coast international volleyed on the rebound to silence the Selhurst Park crowd.
Palace rallied and came close to drawing level on a number of occasions, but the floodgates opened in the 43rd minute of the match as Joe Ledley failed to control a simple knockdown from Damien Delaney, allowing Didier Ndong to claim the ball, take a few strides forward and fire home from 20 yards out.
The Eagles' defence was left exposed moments later when a Sunderland counterattack allowed Adnan Januzaj to race down the left flank in acres of space and loft the ball into the feet of the unmarked Jermain Defoe, who slotted past Hennessey with ease.
Before the half-time whistle had yet blown, the Black Cats had rattled in a fourth, with Defoe claiming his second goal in as many minutes by picking up a cross on the right-hand side of the box, turning past James Tomkins and firing home with his left foot.
The end of the first half saw a backlash from Palace supporters who loudly booed and criticised their team, describing them as "not fit to wear the shirt", while a number of confrontations between Eagles fans and stewards were also reported.
Despite a much-improved second half from the hosts, Sunderland remained strong at the back, with goalkeeper Vito Mannone pulling off a string of fine saves as the visitors refused to let their beleaguered opponents pass.
The final whistle saw the relegation battle blown wide open, with Sunderland remaining bottom of the table on 19 points, level with Palace, while Hull City rounded off the bottom three on 20 points - one behind Swansea City - following their 2-0 win over Liverpool.