Andrew Johnson's 55th-minute strike condemned the Black Cats to their first home defeat in the League this year.
There was a touch of luck about the finish which appeared to hit Johnson on the shoulder before going past Craig Gordon in the Sunderland goal.
However, it was enough to secure all three points for David Moyes' side and keep the Toffees' challenge for fourth place on track.
The goal was a rare bright spot in a fairly miserable afternoon of football with neither side producing any real quality, particularly in a dire first half.
The Black Cats did almost snatch a late leveller but Tim Howard in the Everton goal pulled off a great save to deny Andy Reid in the dying minutes.
Kenwyne Jones also went close for the hosts in the final stages of the game, but his effort was cleared off the line to make sure Everton emerged victorious.
Everton certainly weren't at their best but they did enough to edge the clash with Sunderland offering little in attack. The game ebbed and flowed during the opening 45 minutes but there were no real chances for either side until the half drew to a close.
In the final minutes of the opening period, Tim Cahill went closest to breaking the deadlock. However, after losing his marker to get on the end of an Everton corner the Australian could only watch as his effort came back off the upright.
The half-time interval brought light relief for the crowd of 42,595 as a dour first half came to an end.
Things got marginally better after the break but it wasn't until the 55th minute that there was anything for either set of fans to cheer about.
When the opening did come it fell Everton's way and Johnson made the most of it. Mikel Arteta crossed from the left and former Birmingham City and Crystal Palace forward Johnson left his marker to get the most telling of touches.
The ball seemed to hit the forward on the shoulder before drifting into the net but that won't worry Johnson who celebrated like he meant it.
Sunderland tried to hit back with an immediate riposte but it was a full 11 minutes after Johnson's goal before they created any sort of meaningful opportunity.
Grant Leadbitter played a great throughball for Kieran Richardson but the former Manchester United star could only fire wide from the edge of the area.
The game continued in much the same fashion as the first but Sunderland were ruing their luck in the dying stages.
Substitute Reid looked to have salvaged a home draw when he stepped up to take a free-kick in stoppage time.
The Republic of Ireland international midfielder curled in a wonderful 25-yard free-kick which looked to be dropping just under the crossbar.
However, Howard, who had little to do for most of the afternoon, was more than equal to the test as he made a superb one-handed save to deny Reid.
From the resulting corner Jones flicked the ball on at the near post and looked to have made it all-square only for a last-gasp clearance to put paid to any hopes the striker or his team-mates had of drawing level.
That was the last act for the Black Cats who had frantically tried to get something from the encounter but it wasn't to be as Sunderland's home record came unstuck against the Toffees.