Atletico had looked to have taken a vital buffer into the second leg, when Raul Garcia benefited from a goalkeeper error from Valencia custodian Vicente Guaita.
Guaita's punch attempt from an Atletico corner in the 72nd minute went across the goalmouth to the head of Garcia, who nodded home the game's opening goal at the Mestalla.
Confusion reigned for a brief moment, as Atletico players stormed to central referee Clos Gomez, only to realise he had awarded the goal and not ruled it out for a foul as first thought.
Valencia's push for an equaliser began immediately, with substitute Sergio Canales - who came on in the 73rd minute - testing Atletico goalkeeper Thibaut Courtois with a menacing attempt from range with his left boot that almost curled into the top corner but for a great save from the Belgian.
Atletico had claims for a penalty turned down in the 79th minute, when Diego Costa was seemingly tripped inside the area - only for Gomez to book the striker for simulation.
Valencia, though, would take the momentum into the second leg, when Helder Postiga finished off a fine attacking move in the third minute of additional time.
A dashing run from Andres Guardado down the left side culminated with the Mexican crossing to the far post, where he found second-half substitute Sofiane Feghouli.
Feghouli side-footed the ball back in front of the goal face to the swooping Postiga, who nodded home the equaliser much to the relief of the home faithful.
The return leg takes place at the Vicente Calderon on Tuesday, with the aggregate winner bound for the quarter-finals.
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