But it was a game their hosts should have had sewn up long before Mooney headed in from a Juan Pablo Raponi cross in the final minute.
Cheltenham hit the woodwork no less than four times and spurned a host of other chances to take the lead before a late error by goalkeeper Shane Higgs, whose attempted clearance hit Mooney and fell for Raponi on the left, gave Oxford the chance to claim victory.
The match was spoiled at first by a strong, swirling wind which made it difficult for the players to judge the path of the ball.
Higgs was almost caught out in the fourth minute when a shot from the Argentinian Raponi swerved at him out of the sun. The goalkeeper saw it late and did well to push the shot aside.
Higgs was called upon to make another fine save from Raponi shortly before half-time but, in between those incidents, it was Cheltenham, with the win behind them, who created most of the first half chances.
In fact, they would have gone in at the break wondering how they did not take the lead from a crazy 36th minute pattern of play.
Oxford goalkeeper Chris Tardif could not get strong contact onto his punch from a Martin Devaney corner and Cheltenham's Shane Duff saw a shot cleared off the line from six yards out.
Another corner resulted and again the ball fell to Duff at close range, but this time his shot hit the post. The rebound fell to Steve Guinan who hit the bar and the final shot from Gavin Caines flew over the crossbar.
A marvellously entertaining second half saw a host of chances at both ends with Oxford going close through Raponi and Craig Davies; and Cheltenham's Grant McCann and Devaney forcing good saves from Tardif.
There was even a repeat of the first half goalmouth chaos with 79 minutes gone. McCann saw a shot saved by Tardif, Guinan hit the rebound against the post and substitute Kayode Odejayi even had time to control the ball before smacking his shot against the crossbar.
Duff planted a powerful header from a Devaney corner over the bar but Mooney's late clincher followed shortly afterwards.
Still there was time for Cheltenham to try and get a leveller but defender Caines volleyed a good chance over the bar from a Brian Wilson cross.