Marouane Fellaini struck six minutes from time to cancel out Darren Bent's fine first half header, his eleventh of the current campaign, to extend the Black Cats winless run to six.
The Wearsiders looked to be on their way to ending their barren run when Bent opened the scoring in the 18th minute following excellent work down the right by Kenwyne Jones. But the Toffees deservedly earned a share of the spoils after dominating most of the possession, certainly after the break.
Skipper Lorik Cana returned from a one-match suspension to take his place in the heart of the midfield alongside Jordan Henderson with Lee Cattermole missing our through injury. Paulo Da Silva was also recalled following Michael Turner's four match suspension and he lined up in the middle of the defence alongside John Mensah, with Phil Bardsley replacing Nyron Nosworthy at right back. Kieron Richardson was left out of the match day squad altogether.
Bent should have given the hosts the lead in the sixth minute but headed over, when unmarked, from Andy Reid's free-kick, while Leon Osman struck the outside of the post, two minutes later, for the visitors from just outside the box. Louis Saha shot wide a couple of times soon after while Sunderland striker Jones found the gloves of Tim Howard before the Black Cats found a breakthrough in the 18th minute.
Jones burst down the right and delivered a delicious curling ball that invited Bent to bury, and he did, emphatically, powering a header from eight yards past Howard.
The Trinidad and Tobago international then delivered an almost identical ball three minutes later but Reid got his sums wrong this time and headed back across the goal. Had Bent been on the end of it, it would surely have been 2-0. Lucas Neill headed clear a Reid free-kick three minutes before the break in what was the only other chance of a first half which saw Everton enjoy a large amount of the possession but without hurting Sunderland.
After the break Felliani headed inches wide with only a minute on the clock as David Moyes' team maintained the pressure in the early stages. Saha then shot wide again as the Toffees tried to turn their superior possession into goals.
But the Black Cats were proving just as dangerous on the break and both Bent and substitute Bolo Zenden had efforts to increase the home team's lead around the hour mark. Defender Da Silva then saw his header tipped over by Howard in the 68th minute when getting on the end of another inviting Reid free-kick.
But while it looked as if Sunderland were going to hang on for the three points, Everton's sustained pressure finally found a breakthrough when Tony Hibbert's cross from the right fell kindly to Fellaini from eight yards and he smashed home to level.
There was a late flurry towards the end but no clear opportunities were created and overall, a draw was probably a fair result.
Sunderland: 4-4-2: Fulop; Bardsley, Mensah (Nosworthy, 71) , Da Silva, McCartney, Malbranque (Zenden 58), Henderson, Cana, Reid; Jones, Bent. Subs not used: Carson, Meyler, Healy, Murphy, Campbell Everton: Howard; Hibbert, Neill, Heitinga, Baines, Bilyaletdinov, Osman (Yakubu,70 ), Cahill, Fellaini, Pienaar; Saha (Vaughan 85), Subs: Nash, Neville, Coleman, Duffy Baxter