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.
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.
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.
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.
