Obua said he had appealed to Caf, but that it had backed the Egyptians.
Nine minutes from time, Obua blasted in a long-range effort that skimmed past Boruc's left-hand post.
BBC: SPORT | Football | Scottish Premier | Celtic 2-1 Hearts
And both substitutes played their part in the equaliser as Elliot chased Obua's headed flick-on into the penalty area.
The first meaningful action came midway through the first period when Carey was fouled by David Obua 30 yards from goal.
Michael Stewart returned from suspension for Hearts along with Robbie Neilson, while David Obua and Ruben Palazuelos dropped to the bench.
Kello replaced the injured Janos Balogh in goal and Lee Wallace and David Obua were also restored to the starting line-up.
Immediately after the restart, Obua flashed an effort across the face of Boruc's goal, but the Polish keeper had the angle covered.
BBC: SPORT | Football | Scottish Premier | Celtic 2-1 Hearts
Hearts were starting to come into the game and Obua sent a header from a corner into the turf before the ball trundled wide.
Uganda FA President Dennis Obua said Egypt had offered to pay for the teams' return air-tickets, accommodation and meals, but that they were now back-tracking.
Shortly after the break, Maloney latched on to a Fox cross and stabbed for goal, but David Obua managed to clear off the line to prevent an equaliser.
BBC: SPORT | Football | Scottish Premier | Celtic 2-1 Hearts
Hearts suffered a blow after half an hour when David Obua limped off and the Uganda midfielder's place wide on the right was taken by youth Lithuanian Arvydas Novikovas.
Neilson's long throw-in was missed by David Obua and Driver stole in unmarked to nod home for his fifth of the season and become the club's top scorer this term.
And the dramatic turnaround was completed in the closing stages as Smith failed to gather Templeton's inswinging cross and Obua was on-hand to apply the finishing touch at the back post.
Obua came close to putting the Edinburgh side in front after 66 minutes when he drove in a shot from the edge of the box which St Mirren's Gallacher had to beat away.
The lively Elliot was just out of reach of David Obua's pass in his bid to register a first-half hat-trick and then mis-hit a shot from 18 yards after being teed up perfectly by Driver.
Thomson squandered Hearts' best chance when, after chasing a fine Suso through ball behind the Rangers defence, he waited too long to cross to David Obua and his pass was blocked by goalkeeper Allan McGregor.
Obua passed up an excellent chance to put the ball in the net when his attempted tap-in was blocked by Fraser, but the Hearts man had already been flagged offside shortly before Suso Santana's volley was saved by the Motherwell keeper.
Fraser, who was at fault for the loss of two goals in Motherwell's previous game, spilled a shot by David Templeton but recovered to block David Obua's attempt before Gary Glen relieved the pressure on the visiting defence by firing off target.
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