The Toffees last-season revival was hampered as Seamus Coleman handled inside his area, cancelling out Aaron Lennon's second goal since joining on loan from Tottenham
The in-form Frenchman, who has become Swansea's focal point up front since Wilfried Bony's exit to Manchester City in January, was forced off 16 minutes into a clash that saw the spoils shared following goals from Aaron Lennon and Jonjo Shelvey.
Gomis' withdrawal proved a turning point after early Swansea pressure, with Lennon's calm 41st-minute strike giving Roberto Martinez's men the lead despite having been on the back foot.
Everton appeared on course for a fourth consecutive league win until Seamus Coleman's handball allowed Shelvey an opportunity to equalise from the penalty spot.
Shelvey made no mistake to ensure a stalemate that maintains Everton's unbeaten league record against their Welsh opponents, with Garry Monk's side moving to a record-equalling 47 points for the season.
It takes Swansea level with their haul from 2011-12, with Monk's men having six games remaining to surpass that figure.
Swansea, who brought in Angel Rangel for the injured Kyle Naughton, made much of the early running in a low-key start and saw Gomis go close 12 minutes in.
Gomis brought a smart save out of Tim Howard before his involvement was cut short when he was forced off having appeared to tweak a hamstring.
Marvin Emnes replaced the former Lyon striker and gradually the hosts got back into the ascendancy, with Shelvey beating Howard only to see his effort ruled out for a foul in the build-up.
While Martinez's men struggled to get into their stride initially, Everton finished the half strongly as Seamus Coleman saw a strike saved before Lennon went one better shortly before half-time.
After James McCarthy's cross evaded two Swansea defenders, Lennon lost marker Neil Taylor and angled an effort into the far corner to register his second goal for the club since joining on loan from Tottenham.
Monk's side set about finding their way back into the game after the break and were gifted an opportunity when Coleman handled inside the area under pressure from Emnes.
The substitute harried the Everton man into an inexplicable handball and Shelvey tucked home the equaliser shortly after the hour mark.
McCarthy wasted an opportunity to have the final say, when he opted to pass to Lennon instead of shooting in the final third, before Gylfi Sigurdsson curled a free-kick narrowly over the crossbar for the hosts.
However, both sides left with a point apiece, as Everton edged closer to Premier League safety, while Monk will hope for a positive prognosis on Gomis' fitness going into the final few games of another positive campaign.