Sunderland 0 Everton 1: A slice of luck for Andrew Johnson at Sunderland was enough to hand Everton the points and keep alive their hopes of edging Liverpool out of the Champions League places.
Johnson scored the only goal of the game when Mikel Arteta's left-wing cross ricocheted off his arm in the 55th minute, leaving their committed but limited opponents still nursing relegation worries.
The striker had earlier missed a gilt-edged opportunity to open the scoring, heading over from point-blank range when Tim Cahill's effort was cleared off the line by Anthony Stokes.
The Black Cats pressed Everton from the off and both Tony Hibbert and Joleon Lescott were fortunate to get away with poor touches at the back.
There were appeals from the crowd for a home penalty when Stokes' cross from the right was blocked by a jumping Lescott, but there were no obvious signs of handball.
Kenwyne Jones then pressured Tim Howard under a high ball but his presence was little more than nuisance value as clear opportunities remained thin on the ground.
Phil Bardsley ensured that remained the case after 26 minutes, sliding in full-blooded on the edge of his area to deny Stephen Pienaar time to shoot.
That enthusiasm bubbled over soon after, with Bardsley fouling Arteta on the left. More worryingly, though, was what appeared to be a kick aimed at the floored Spaniard by the incoming Stokes.
Cahill then had the chance to send the visitors in ahead at the break but failed to beat Stokes on the line.
Stokes had no further chance to impress, manager Roy Keane sending on Michael Chopra for the second period.
The Black Cats restarted with a better tempo and after 47 minutes, Daryl Murphy's whipped cross narrowly failed to find the leaping Jones at the far post.
Kieran Richardson, like Bardsley a former Manchester United player, soon had his first real impact, surging through the middle of the park and releasing Murphy with a cross-field pass.
The Irishman, with just Hibbert to beat, showed too much of the ball to the right-back and the danger evaporated.
It looked like it would take a piece of luck to make something happen and it came when Arteta sent a searching cross into the Sunderland penalty area, with Johnson lurking.
At least three bodies surged towards the centre but it looked as though the final touch came from the former Crystal Palace striker's shoulder and the ball sailed over Gordon and into the net.
As Sunderland's response faltered, Murphy was dispossessed just outside his own box, conceding a free-kick as he tracked back. Johnson created space 10 yards out from Arteta's delivery but Nyron Nosworthy's last-ditch tackle smothered his shot.
By now, the hosts were looking to Jones for inspiration and, with 19 minutes remaining, he came to life. He powered through the Everton midfield with a muscular run but eventually ran out of steam with three blue shirts surrounding him.
Keane used his final substitute in the 75th minute, striker Rade Prica joining Chopra and Andy Reid in coming from the bench.
But despite the increased attacking options, Sunderland could find no way past Everton, Chopra seeing his first shot blocked by a defender.