Valencia remained unbeaten in two games under new coach Juan Antonio Pizzi.
Valencia kept the action in Atletico's half for most of the game, without letting Atletico striker Diego Costa roam free on the break. After a stalemate in the first 45 minutes, it needed all Courtois' goalkeeping skills to keep Sergio Canales, Pablo Piatti and Sofiane Feghouli from scoring.
But Courtois could do nothing when Canales played the ball wide for Feghouli to cross to the unmarked Postiga for the last-gasp goal.
"I think we deserved a little more, but we got the equalizer and the tie is wide open," Postiga said.
The second leg will be played in the Spanish capital next Tuesday.