Marouane Fellaini took a pass from Leon Osman at the edge of the box and turned to dispatch a low shot through John O'Shea's legs into the bottom corner with 14 minutes remaining.
And Osman was the instigator again when his threaded pass was flicked inside the penalty area by Fellaini where Nikica Jelavic pounced to tuck the ball under the advancing Simon Mignolet.
Adam Johnson (45) had given Sunderland a deserved lead when he reacted quickest to Craig Gardner's looped delivery into the box and caught the ball on the drop to place past Tim Howard.
Sunderland created an early chance when Steven Fletcher threaded a pass inside Seamus Coleman to Stephane Sessegnon and his low drive was blocked by Howard's left foot.
The Sunderland duo combined again and this time Fletcher beat Howard with his low angled shot which slid past the far post.
Steven Pienaar stung the palms of Mignolet with an angled shot before the Sunderland keeper got down and prevented a low cross from the same player reaching Fellaini inside the six-yard box.
Jack Colback then shot weakly at Howard from eight yards as Sunderland worked another opening shortly before the diving Mignolet punched a long range drive from Phil Neville away at the other end.
Everton's enjoyed a period of pressure after the break and were denied an equaliser when Johnson cleared a header from Johnny Heitinga off the line after the defender rose to meet a Leighton Baines corner.
But the hosts would not be deterred and were rewarded for a dominant second half performance with those two swift goals.
|0||1st Half Goals||1|
|6||Shots on Target||3|
|6||Shots off Target||3|
|64.9||1st Half Poss.||35.1|
|58.7||2nd Half Poss.||41.3|