A second-half penalty from Jonjo Shelvey earned Swansea a point as Everton’s three-game winning run in the Premier League came to an end.
Shelvey, who had a spectacular first-half effort disallowed following a foul in the build-up, slotted home after Seamus Coleman had carelessly handled.
On-loan winger Aaron Lennon had fired Everton ahead from a James McCarthy cross four minutes before the break.
Swansea equalled their record Premier League points tally of 47.
Everton, who had lost 3-0 at the Liberty Stadium in the League Cup earlier this season, are still the only side Swansea have never beaten in the league.
Having won their previous three league games, the Toffees’ manager Roberto Martinez kept faith with the team which beat Southampton in their last game.
Everton top-scorer Romelu Lukaku was still missing through injury and Swansea were soon without their leading striker too, as Bafetimbi Gomis was taken off after just 16 minutes clutching his hamstring.