Everton’s back-four dropped deep to negate the threat of the ball over the top for Defoe, but the forward lifted the flagging atmosphere when he almost blocked a hurried Robles clearance form inside the area after he was sold short by an awful back-pass from Ramiro Funes Mori. With the crowd back involved, Younes Kaboul went close with a low curling effort as he popped up in an unexpected attacking position.
His defensive colleagues Van Aanholt and Kone showed him how it should be done soon after to put the hosts within reach of survival.
Kone came close to adding a third straight after the break after causing more carnage in the Everton box at a corner, while Defoe almost claimed the goal his brilliant display deserved as Pennington cleared his effort off the line.
Everton were hanging on and it came as no surprise when the third goal arrived in the 55th minute, Kone given time and space two yards out to thrash the loose ball home after Robles made a hash of Khazri’s inswinging corner.
Funes Mori and Barry forced late saves from Vito Mannone, but by then the escape party celebrations had long since started.
Sunderland (4-1-4-1): Mannone; Yedlin, Kone, Kaboul, van Aanholt; Kirchhoff (Larsson 68); Borini, Cattermole (O’Shea 78), M’Vila, Khazri (Watmore 85); Defoe.
NEXT UP: Watford (a), Sun PL.
Everton (4-2-3-1): Robles; Pennington, Stones, Funes Mori, Baines; McCarthy, Barry; Mirallas, Barkley (Lennon 46), Cleverley (Osman 83); Lukaku.
NEXT UP: Norwich (h), Sun PL.
Referee: A Taylor (Wythenshawe).