Atletico, who won the cup for the first time since 1996 last season when they upset local rivals Real 2-1 in the final at the Bernabeu, had looked set for a narrow advantage thanks to Raul Garcia's 68th-minute goal and three fantastic late saves from Thibaut Courtois.
However, with three minutes of added time played, Postiga headed home from close range as Courtois was finally beaten.
It was Courtois' opposite number Vicente Guaita who had been earning all the attention before then, as he produced a superb one-handed save to keep out Garcia's piledriver during a goalless first half before then making a glaring error for Atletico's goal.
Guaita made a complete mess of trying to punch clear a corner from inside his six-yard box and Garcia had the simplest of tasks to head home from just a couple of yards out.
After that it was pretty much all Courtois as Valencia desperately sought an equaliser.
The on-loan Chelsea keeper made the save of the match in the 76th minute when he clawed away Sergio Canales' 25-yard curler that looked destined for the far top corner.
Six minutes later the Belgium international made another top-drawer save to keep out Pablo Piatti's low drive, with Canales blazing the loose ball over the bar.
Then moments later Courtois was called upon again to parry a shot from Sofiane Feghouli after the Algeria international had sliced through the Atletico defence with a mazy run.
Those saves looked set to earn Atletico a first-leg advantage, but Valencia managed to find a leveller when Feghouli volleyed Canales' deep cross back across goal and Postiga nodded in from six yards out.