Own goal decides Wearside clash.
Sunderland slipped to an agonising defeat they did not deserve as Everton notched a seventh straight league win.
The Black Cats produced some of their best football since the Capital One Cup final, but were denied by an unlucky own goal by Wes Brown.
The defender saw Gerard Deulofeu's 75th-minute cross strike him and spin into the net after Gus Poyet's side had matched the in-form Toffees yard for yard.
Sunderland, who now have six games remaining, created several opportunities but couldn't get beyond Tim Howard.
When they did, they were still denied, with John Stones clearing Fabio Borini's goalbound shot off the line in the first half.
Ahead of the game, captain John O'Shea and midfielder Jack Colback both returned to the side in place of Carlos Cuellar and Santiago Vergini.
Meanwhile expectant father Liam Bridcutt missed the game with his wife in labour – Connor Wickham taking his place in the starting XI.
The game kicked off seven minutes later than usual as part of the commemorations to mark the 25th anniversary of the Hillsborough stadium disaster.
Sunderland got off to bright start, but it was the visitors creating the clear-cut opportunities.
Colback did well to hold up Deulofeu on a 10th-minute break with Vito Mannone holding the resulting shot, while Steven Naismith wasted an excellent opportunity to give the hosts the lead soon afterwards.
The Scot produced an excellent turn to outfox Brown as he met Leighton Baines' low pass just inside the box, but the frontman's wild shot was too high with the goal at his mercy.
Romelu Lukaku then fired straight at Mannone as the visitors, looking to move into the Champions League places, began to exert their influence on proceedings.
Having soaked up considerable pressure, Sunderland responded by almost taking the lead on the break just after the half-hour.
Following neat control from Wickham, Baines' backpass was intercepted by Borini who swept beyond Howard, but defender Stones was back quickly to block the striker's effort from a narrow angle.
And the Black Cats were the better side going into the break, with Wickham proving a handful up front and seeing a powerful drive blocked before Johnson's cross-shot was similarly repelled by the Everton defence.
Backed by a noisy crowd, the hosts continued to ask questions in the second half, with the ball being hacked away in a scramble after a Phil Bardsley header was blocked inside the six-yard box.
Ki then headed just wide at the back post, though Everton carried a threat on the break and Naismith fired into the side-netting after Mannone was forced to advance from goal to head the ball clear.
The Italian then made a good save to deny sub Ross Barkley, palming the ball away by his left-hand post after the England man snuck in to meet a deep cross.
At the other end, Marcos Alonso's powerful drive was met with an equally good save from Howard before the Toffees struck what would prove to the winner.
Deulefou got down the line beyond Alonso and attempted to pull the ball back, but to the hosts' horror the ball struck Brown and sneaked in between a wrong-footed Mannone and the post.
It would be a cruel way to lose any game.
Nonetheless, the hosts kept going as Howard denied Ki, who then saw a shot on the turn flash over the bar with nine minutes to go.
Howard was on hand again to save a Wickham effort from outside the box, and the Everton keeper was then relieved to see Borini's 25-yard blast sail inches past the upright with five minutes to go.
But the ball just wouldn't go in for Sunderland, who saw Howard gather Johnson's free-kick in stoppage time as the visitors moved into the top four.
- Yellow Bardsley
- Colback (Larsson)
- Yellow Johnson
- Distin Yellow
- Coleman Yellow
- Deulofeu (McGeady)
- Osman (Barkley)
- Yellow Larsson