The first two thirds were forgettable, but stunning blasts from Seamus Coleman and Ross Barkley see Everton burgle all three points from Liberty Stadium.
With both teams playing a possession game early, the first 65 minutes could have put some to sleep, but Coleman had a go from distance and rocketed the game awake.
Swansea then equalized just minutes later thanks to a deflection, but a thunderous free kick from Ross Barkley put the visitors into the lead for good.
Everton began the match on the front foot, looking to build from the midfield with lots of passing and possession, but Swansea’s defense proved difficult not only to unlock but even budge.
From the start, both teams settled into possession, and very little was created in the first half. The ball rarely even found its way into either attacking third, with both teams trying to work from the back up.
The only real opportunity in the first half came as Gerhard Tremmel spilled a catch directly at the feet of a surprised Lukaku, but the big striker whiffed and Tremmel collected safely.
Basically nothing happened in the first 45 minutes, with neither goalkeeper required to do much, if anything.
The second half proved similar, although a few chances came begging. Fittingly, rain began to fall around the 55th minute, and it saw Coleman weave through the Swansea defense in a Lionel Messi-esque run but it was cut out one defender before he reached the goal.
Finally, a quality attempt on goal came to pass in the 65th minute. Barkley sliced through open space in the Swansea midfield, shook a defender with a touch to his left, and rattled the crossbar off the fingertips of Tremmel.
That was a sign of things to come for Everton, as Coleman minutes later worked some space well outside the 18-yard box, and blasted a thunderbolt past a wrong-footed Tremmel and into the back of the net. It was a true stunner by the 25-year-old defender for his fourth goal of the season.
The style of play wasn’t changed for either side following the goal, but Swansea would also find something out of nothing for their equalizer just four minutes later.
A cross from Ben Davis floated in, and Dwight Tiendalli didn’t get a clean shot off, but the resulting effort caromed off Brian Oviedo and left Tim Howard no chance. The official word came down as an own-goal on Oviedo, as Tiendalli’s original shot was going a decent way wide.
The final 10 minutes saw some chances as both sides pressed for a winner. Substitute Alvaro Vasquez brought the ball down the right side of the box on his own, but with no support his chip attempt went right into the waiting arms of Howard.
Then it was the youngster’s moment. With Davies having scythed down James McCarthy outside the box, 21-year-old Barkley ripped a strike into the top corner for the winner.
The American keeper had to make a pair of excellent saves in the final few minutes, with Swansea pouring forward, but the Everton defense held well.
The win for Everton means they stay unbeaten in 10 straight, and travel into the top four of the Premier League table jumping Chelsea, who play tomorrow.
Swansea have just two points in their last three matches, and remain in 11th place level with Hull City on points.
Everton – Coleman 66′, Oviedo 70′ (og), Barkley 84′
Swansea – Tremmel; Tiendalli, Chico, Williams, Davies; Canas, Shelvey, de Guzman (Pozuelo 86′), Routledge (Lamah 66′), Hernandez; Bony (Vazquez 76′).
Everton – Howard; Coleman, Jagielka, Distin, Oviedo; Mirallas (Osman 78′), McCarthy, Barry, Pienaar (Naismith 78′), Barkley; Lukaku.