In a chaotic week that saw the Tannadice club knocked out of the Europa League by AEK Athens, Gomis struck an unstoppable 25-yard drive high into the net to cancel out David Templeton's first-half goal.
The equaliser came minutes after Hearts goalkeeper Marian Kello saved Jon Daly's spot-kick.
Following an exhausting midweek trip to Greece, United's plans at Tynecastle were disrupted as early as the third minute when Danny Swanson pulled up clutching his hamstring after a bursting run from midfield and was replaced by David Robertson.
In the football that was played during the early stages, the hosts fashioned the first chance after five minutes.
Templeton teed up Kevin Kyle outside the box but the marksman blasted a shot well over Dusan Pernis' crossbar.
United were struggling to deal the Kyle's height advantage with the striker winning just about everything in the air.
Craig Thomson's cross was knocked down by the former Kilmarnock player but Adrian Mrowiec's effort glanced off the top of the bar.
United threatened for the first time when Barry Douglas swung a dangerous low cross into the six yard box and Kello did well to get to the ball ahead of Daly.
Hearts winger Templeton then unleashed a stinging left-footed drive from an angle inside the box that was pushed behind by Pernis.
The home side invited pressure on themselves through slack defending that culminated in the hosts conceding a corner just as David Goodwillie was about to pull the trigger inside the box.
However, from the resulting set-piece Hearts broke on the counter-attack and took the lead through Templeton in the 30th minute.
Santana raced clear of Garry Kenneth from deep inside his own half before finding Templeton charging into the box.
The winger's heavy first touch looked to have narrowed the angle with Pernis rushing from his line but he slipped a delicate right-footed reverse shot into the corner of the net.
United carved open the Hearts defence three minutes before the break when Daly powered forward and teed up Craig Conway. But the sought-after midfielder blazed a shot over the bar from inside the box.
In a scrappy start to the second half, Goodwillie beat the offside trap but any advantage he had on the Hearts defence was lost when he cut inside and was fouled by Darren Barr.
Douglas stepped up to take the free-kick 20 yards out but his poor left-footed effort was blocked by the wall.
At the other end, Templeton cut out a Keith Watson pass and had room to run at the United defence. After making his way to the edge of the area, the former Stenhousemuir player struck a right footed shot that was deflected just past the post.
Conway was without doubt United's most dangerous player and he hit a left-footed drive from 20-yards just over after spinning away from Eggert Jonsson on the edge of the area.
United were handed a chance to level when referee Craig Thomson pointed for a penalty after spotting a handball in a congested box.
Skipper Daly stepped up to take the spot kick but his tame effort was palmed clear by Kello to the delight of his team-mates.
Before United could take the resulting corner, the referee appeared to send off Hearts coach Gary Locke from the technical area.
The visitors were level four minutes from time, however, when substitute Gomis struck a stunning 25-yard strike high into the net.
David Robertson's cross was only partially cleared and Gomis pounced with a half-volley that flew into the top corner.
United finished the game on the front foot as Conway cut inside in the box before having a shot repelled by Kello.