The defeat, which came via a brace from Toffees striker Jermaine Beckford, was the Black Cats' fourth on the bounce.
It was arguably the worst of the four, with Steve Bruce's side struggling to carve out chances after Stephane Sessegnon hit the woodwork midway through the first half.
Bruce made three changes to the side that had lost to Tottenham, with Simon Mignolet replacing Craig Gordon in goal and Anton Ferdinand and Ahmed Elmohamady both returning to the starting line-up.
The Black Cats started with a five-man midfield, and one of their midfielders, Kieran Richardson, should have given them the lead after five minutes.
The England international was released by an excellent through ball from Asamoah Gyan, but skewed a 14-yard shot horribly wide of the target.
The miss proved costly, as Everton broke the deadlock themselves three minutes later. Leon Osman's through ball sent Beckford running behind a static Sunderland defence, and the striker's shot beat Mignolet with the help of a hefty deflection off Titus Bramble.
Sessegnon came within inches of an equaliser midway through the first half, but Everton goalkeeper Tim Howard turned the Frenchman's rising drive onto the underside of the crossbar.
The hosts then doubled their lead with six minutes of the opening period remaining. Mikel Arteta beat both Anton Ferdinand and John Mensah as he dribbled towards the byline, and Beckford scrambled home the Spaniard's cut back from close range.
Beckford and Osman both went close for Everton at the start of the second half, and Bruce introduced teenage striker Ryan Noble shortly after the hour mark in an attempt to change the game.
However, the change had little effect as Sunderland still struggled to retain possession in Everton's half of the field.
Indeed, the defeat would have been heavier had Elmohamady not headed Osman's goal-bound shot off the line in stoppage time.
EVERTON (4-4-2): Howard; Neville, Jagielka, Distin, Baines; Coleman, Fellaini (Rodwell 42), Arteta, Osman; Beckford (Cahill 73), Saha (Bilyaletdinov 82).
Subs (not used): Mucha (gk), Hibbert, Heitinga, Baxter.
SUNDERLAND (4-5-1): Mignolet; Ferdinand (Noble 67), Bramble, Mensah, Bardsley; Elmohamady, Henderson, Muntari (Malbranque 77), Richardson, Sessegnon; Gyan.
Subs (not used): Gordon (gk), Knott, Zenden, Riveros, Colback.