The French striker has been challenged to grasp his first-team chance in the absence of Wilfried Bony, who has departed for the Africa Cup of Nations with Ivory Coast while rumours of an imminent transfer to Manchester City persist.
And, after Andy Carroll had opened the scoring with a superb left-footed strike two minutes before half-time, Gomis was instrumental in Swansea's equaliser.
Gomis rose highest from a Gylfi Sigurdsson corner to head across goal in the 74th minute, with Mark Noble inadvertently touching the ball into his own net.
The former Lyon man Gomis produced a French flag as he celebrated his leveller in an apparent tribute to the victims of the recent terror attacks in his homeland.
The result sees Swansea and West Ham remain ninth and seventh respectively in the Premier League.
Assistant manager Neil McDonald stood in for the unwell Sam Allardyce in the West Ham dugout, but the London club were sent to Swansea with a new formation – starting with three across the back, flanked by wide men Carl Jenkinson and Aaron Cresswell.
Despite including three central defenders in their starting XI, West Ham almost allowed Gomis to weave his way through the middle of their backline inside the opening five minutes.
The France international's eventual strike was deflected into the path of Nathan Dyer on the right, but Gomis was unable to get his head to a dangerous cross from the winger.
Ashley Williams – making his 300th Swansea appearance – appeared to haul Enner Valencia to the ground in the build-up to a West Ham free-kick, although the home captain escaped with a talking to, before Gomis drew a routine save from Adrian with a low drive from distance.
West Ham kept their hosts quiet in the opening stages and had chances to break the deadlock themselves inside half-an-hour – Jenkinson blasting over, while Kevin Nolan narrowly cleared the crossbar with a shot from the edge of the box.
Wayne Routledge then sent Gomis clear as Swansea went in search of an opener, but the striker checked his run twice before showing too much of the ball to James Tomkins.
Sigurdsson, who was uncharacteristically anonymous for much of the first half, fired a tame effort straight at Adrian in the 38th minute, before Carroll broke the deadlock at the other end.
The towering striker picked the ball up in the box and turned to face goal, before rifling a left-footed effort into the corner from 18 yards, although the visitors had a last-ditch Jenkinson challenge to thank for denying Routledge an almost instant reply.
Sigurdsson curled just wide from 25 yards within 30 seconds of the restart, but it was West Ham who looked most likely to find the net.
Gomis squandered a golden opportunity shortly before the hour when he blasted over following a throughball from substitute Marvin Emnes, but he atoned for that miss in the 74th minute.
Noble made a mess of his attempts to clear Gomis' header off the line, diverting the ball into the net to restore parity.
West Ham twice went close to snatching the three points in the closing stages - Stewart Downing drawing a great save from Lukasz Fabianski, before Carroll fired wide after the Polish goalkeeper had parried a Cresswell free-kick - but Swansea held on for a share of the spoils.
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