Goals from Patrick van Aanholt and a double from Lamine Kone saw them seal safety in style, with a clean sheet topping things off in a magical night on Wearside.
Comfort and celebration on Wearside
Sunderland gradually started to be an attacking threat in the game; Younes Kaboul producing their first effort on goal with a header while Everton had the majority of the possession the opening 10 minutes.
Kaboul went close again at the midway point of the half. Producing a quick run-down the left wing, the Frenchman curled in a shot which drifted just wide of the far post.
But after 38 minutes, during which Sunderland struggled to create chances, the Black Cats went ahead through a van Aanholt’s free kick which left the stadium in joyous amounts of noise.
Moments later, the sea of red and white fans were out of their seats when Jermain Defoe forced a superb tip over the bar of out Joel Robles.
But from the resulting corner, the Black Cats doubled their lead. Everton failed to clear their lines from Wahbi Khazri’s corner and Yann M’Vila headed back to Kone, played onside by Leighton Baines, who smashed in a volley which almost burst the net and left Robles flabbergasted.
Last ditch defending from Matthew Pennington prevented Defoe adding a third after the striker was picked out by a well-timed through-ball from DeAndre Yedlin.
However, from another corner, Sunderland did in fact add a third as an embarrassing Everton defence was troubled by another set piece.
Khazri almost scored direct from the corner as a desperate Robles palmed it away but, unfortunately for the Toffees, it bounced off his own player and straight into the path of the eagerly anticipating Kone, who tapped in from a few yards out.
Agonisingly for Defoe, he was denied again for a fourth goal in the 66th minute. Van Aanholt threaded him through and the striker brought it under control before firing a powerful shot towards the near post, which was pushed away by Robles.
It wasn't plain sailing for the Black Cats as Vito Mannone proved he deserves his spot in the team; brought to action when he tipped away Ramiro Funes Mori’s header from a Baines’ free-kick.
Despite dominating possession for large parts of the match, it was only in the closing stages of the gam that Everton truly threatened. Kevin Mirallas twice went close while Romelu Lukaku thundered a shot from close range which rattled the bar, but it was all in vain as Sunderland secured three points which ensure safety once again.