Dong-Won Ji scored on the final kick of 0 win over Manchester City at the Stadium of Light on Sunday.
With Manchester United having lost 3-2 to Blackburn on Saturday, City had the chance to move three points clear at the top of the league.
However, the visitors were twice denied by the crossbar and wasted numerous scoring chances before being punished by Ji at the death.
Edin Dzeko had the first chance to put City in front just after the half-hour mark when his close-range effort was parried by goalkeeper Simon Mignolet.
Adam Johnson then beat Mignolet with a low shot but his effort was cleared off the goal line by Sunderland's Craig Gardner.
City continued to pressure and came within inches of taking the lead when Dzeko's shot from just inside the penalty area crashed off the crossbar.
Sergio Aguero forced an awkward save from Mignolet just before the hour mark, while Sunderland's Stephane Sessegnon shot just wide with only goalkeeper Joe Hart to beat in a rare chance for the hosts.
City turned up the pressure as the match entered the final 10 minutes and they nearly found a goal in the 88th minute when David Silva's shot was parried by Mignolet into the path of Micah Richards, who headed the rebound off the crossbar.
Despite being pinned back for a large portion of the match, Sunderland put together a late counter attack that resulted in the winning goal as Sessegnon played Ji into the area and the South Korean rounded Hart and rolled the ball into the net.
Everton 1, West Bromwich 0
West Bromwich, England - Victor Anichebe came off the bench to score three minutes from time, giving Everton a 1-0 win over West Bromwich at the Hawthorns on Sunday.
Both sides struggled to carve out chances in the opening half before a good opportunity fell to West Brom's Peter Odemwingie in the 47th minute.
Anichebe replaced Phil Neville midway through the second half and he was on hand in the 87th minute to slot home the winner after the West Brom defense failed to deal with a Tony Hibbert cross.
The win moves the Toffees above West Brom in the table and gives Everton eight points from its last four games.