Toffees lose unbeaten home record
Sunderland gave their Barclays Premier League survival hopes a much-needed boost with a 1-0 victory over 10-man Everton at Goodison Park.
A 25th-minute penalty from on-loan Swansea midfielder Ki Sung-yueng steered the Black Cats to what was their first victory in seven top-flight matches.
The spot-kick was awarded after Leon Osman miscontrolled a goal-kick from Tim Howard.
Ki latched onto the ball and darted into the box, where he hit the turf when tackled by Howard, who was shown a straight red card.
Everton, with Ross Barkley on as a substitute, piled on the pressure after the break but could not find an equaliser, with Sunderland goalkeeper Vito Mannone pulling off several impressive saves.
Gus Poyet's men remain bottom of the table, but have cut the gap between them and safety to three points.
The Toffees, meanwhile, remain fifth after what was only their second league defeat of the season.
There was a nervous moment at the back for Everton early on when their skipper Phil Jagielka misjudged a header and Steven Fletcher looked to take advantage, but they survived as Howard rushed out to clear.
There were then optimistic efforts struck from distance at both ends, with Fabio Borini sending one over Howard's bar before Bryan Ovideo cut inside and cracked the other towards Mannone, who got behind it.
Moments later, the Toffees won a corner, via an Oviedo cross, which Gareth Barry met with a header but could not guide on-target.
James McCarthy scuffed a shot into the stand and when his fellow Everton midfielder Barry then gave away possession, Sunderland worked the ball to Jack Colback, whose low strike was saved by Howard.
It was not long after that when the goalkeeper received his marching orders having opted to play a goal-kick short to Osman.
Osman made a hash of attempting to control it and Ki claimed possession, looked to go around Howard and went to ground in the area when the United States international came out to meet him.
Referee Lee Probert had no hesitation in pointing to the spot and sending off Howard, who was replaced in goal by Joel Robles - brought on by Toffees boss Roberto Martinez for Osman.
And Ki, scorer of Sunderland's winning goal in their recent Capital One Cup quarter-final win over Chelsea, then made no mistake in firing the penalty in past Robles, who was on his Everton Premier League debut.
Robles looked shaky as he fumbled an Ondrej Celustka drive in the 36th minute but did well to block the follow-up by Sebastian Larsson and from the resulting corner, Ki miscued wildly when trying to shoot.
Everton then found themselves down to nine men for a few minutes, with Kevin Mirallas having headed down the tunnel, and when the Belgium forward returned to the pitch, Barry picked up a booking - meaning he will be suspended for the next match - for a tackle on Colback, with Larsson then curling the subsequent free-kick over.
Mirallas was substituted at the interval for Barkley, and after coming through a spell in which Modibo Diakite scooped a deflected effort over and Fletcher's header was saved by Robles, Everton began to apply some pressure of their own.
Mannone made a decent parry to keep out a Jagielka header and got his hands on Romelu Lukaku's attempt at a rebound shot.
Lukaku then saw Mannone get down to claim his drilled shot from outside the box, before Barkley - who netted so spectacularly in the previous game against Swansea - sent another ambitious effort too high.
Fletcher brought a save out of Robles, but Everton kept pressing, with Barkley looking in increasingly confident mood as he drew a parry out of Mannone and then struck narrowly wide.
Mannone comfortably dealt with further shots from Lukaku and Barkley, then produced a delightful save to push behind a rising drive from Oviedo.
There was a brief respite for the visitors and Fletcher dragged an attempt the wrong side of the post having been put through.
But Everton were soon pressing again, and Mannone did superbly to palm away Barkley's free-kick as the England international tried to repeat his match-winning trick from the Swansea contest.
The Toffees came close again as the end of the game drew ever nearer, with Borini clearing an effort from substitute Nikica Jelavic off the line, before the final whistle confirmed Sunderland had held on for all three points.