0-1, min. 17, Sigurdsson. 1-1, min. 26, Cork (og). 1-2, min. 34, Ayew.
Swansea City recorded their first league victory at Goodison Park as Everton failed to end a two-month run without a league win on home soil.
A Gylfi Sigurdsson penalty, after a mix-up between John Stones and Tim Howard, gave Swansea the lead before a Jack Cork own goal drew Everton level.
Andre Ayew's deflected strike 10 minutes before half-time proved to be the winner, as Everton failed to convert their chances in the second-half.
A defensive error allows Swansea to claim the advantage
Swansea had never previously led against Everton in a Premier League game, but they managed it twice in the first-half meaning that Everton would have to score at least three goals to win the game.
It was Everton who came close to taking the lead in the fourth minute of the game, when Muhamed Besic saw his shot from outside the area hit the post after driving forward with the ball from the halfway line.
The shot proved to the sum total of Besic's involvement as the Bosnian was replaced by Tom Cleverley in the 10th minute after he was forced off with what looked like a reoccurrence of his hamstring injury.
The mood inside Goodison Park soured further after a defensive error allowed Swansea to claim the advantage in the 17th minute from the penalty-spot.
Andre Ayew was brought down by Tim Howard in the penalty area, but it must be John Stones who takes the lion's share of responsibility. The 20-year-old's backpass was too short for the hesitant Howard and Ayew beat the Everton goalkeeper to the ball, before being brought down in the box.
Gylfi Sigurdsson sent Tim Howard the wrong way, slotting his penalty emphatically into the top left-hand corner to silence the Everton faithful in Goodison Park.
Everton equalise, but more misery followed
Swansea's lead lasted 11 minutes when Jack Cork turned Gareth Barry's flick from Gerard Deulofeu's corner into his own net, but the Blues were dealt another blow as Kevin Mirallas was forced off with an injury in the 27th minute.
The goal seemed to settle any lingering nerves, with Everton showing more urgency and the introduction of Steven Pienaar, who replaced Mirallas, helped give Everton more balance to their play, however this did not last long.
Roberto Martinez's side were level for less than eight minutes before Andre Ayew restored the visitors' lead. Left-back Neil Taylor played the striker in and Ayew's left-footed shot deflected off Stones' outstretched leg and beyond Tim Howard.
Everton's players switched off after claiming for handball and they will feel aggrieved as replays showed that Ashley Williams did handle the ball in the build-up. It was almost an immediate response from the Blues as Lukaku ran at goal, but his shot went narrowly wide.
The half-time whistle was greeted with boos from some Everton supporters at a nervy, worried and angry Goodison Park after their side's first-half showing.
Everton dominate, but fail to convert chances
Everton started the second-half strongly, although Ross Barkley will have been glad that he was offside after he fired over from less than six yards.
Gerard Deulofeu has so often produced the spark that Everton have needed this season and he nearly provided the inspiration that the Blues needed to draw back level.
Steven Pienaar failed to hit the target from Gerard Deulofeu's dangerous cross, before another delivery from the Spaniard flashed across the goal, with no one there to provide the clinical touch.
As Everton committed more men forward to try and find an equaliser, the game started to open up. Tim Howard had to stay alert to deny Gylfi Sigurdsson, before Romelu Lukaku saw his curling effort go just wide at the other end.
Everton continued to dominate, but could not find an equaliser. Lukaku produced a smart save from Lukasz Fabianski with his header, after great work from Ross Barkley, before substitute Seamus Coleman fired over the bar from two yards out with the very last kick of the game.
