After Adnan Januzaj’s effort ricocheted off Idrissa Gueye, the ball dropped over Defoe’s shoulder but he could only scoop it over the bar from 12 yards out.
Lynden Gooch’s cross-shot was turned over the top by Stekelenburg before half-time but the Black Cats were a beaten side the moment Lukaku pounced.
Sunderland hadn’t won a league game in August or September since 2012, a wretched run of 22 games which had shaped their subsequent campaign and after another false start, the pattern looks entrenched.
Sunderland (4-2-3-1): Pickford; Manquillo, L Kone, Djilobodji, Van Aanholt; Kirchhoff (Denayer 76), Rodwell; Januzaj, Gooch (Khazri 57), Watmore (Ndong 73); Defoe. Subs: Mika, O’Shea, McNair, Love.
Everton (4-2-3-1): Stekelenburg; Coleman, Williams, Jagielka, Baines; Gueye, Barry; Bolasie (Davies 75), Barkley (Deulofeu 46), Mirallas; Lukaku (A Kone 88). Subs: Robles, Lennon, Funes Mori,Holgate.
Referee : Mike Jones