The Toffees welcomed back Idrissa Gueye in place of Tom Davies after the midfielder’s substitute appearance last weekend.
However, his return failed to add anything to the Blues’ midfield as the hosts started the strongest.
Swansea should have been ahead during a dominant spell in the first period but Leighton Baines and Cenk Tosun were alert to clear efforts off the goal line.
By this stage Swansea had attempt eight shots at goal, Everton none, as the dour, negative style under Sam Allardyce continued.
You had to laugh therefore when Everton took an thoroughly undeserved lead just before the break thanks to a truly comical own-goal by Kyle Naughton.
That should have given Everton the platform to push for victory in the second half, with the desperate Swans likely to commit more men forward in an attempt to equalise.
Everton were slightly better after the break, but they were far too cautious and rarely troubled Swansea ‘keeper Lukasz Fabianksi.
It was no surprise therefore when Swansea equalised through Jordan Ayew, even if it stemmed from a ropey Seamus Coleman clearance and a wayward shot from Tom Carroll.
That prompted Allardyce to return to type as he brought on defender Ramiro Funes Mori for forward Yannick Bolasie with 14 minutes left, meaning we ended the game with five defenders and two defensive midfielders.
It was great to see Funes Mori back in the pitch after more than a year out but it was hardly the most inspiring change for supporters hoping for a rare away victory.
Coleman nearly snatched the win when he smashed the crossbar from Tosun’s right-wing cross but it would have been an undeserved three points.
The result will do little to appease the growing dissent amongst Evertonians towards Allardyce, with the travelling supporters even calling for the former England boss to go now.
That is unlikely to happen, unfortunately. But at least this is one more game to scratch off the list before the end of the season.