Early goals from Karl Toko Ekambi and Alfonso Pedraza put visitors Villarreal in control at Balaidos, before a stunning second-half turnaround earned Fran Escriba his first win as Celta coach.
Aspas, who last started a game in December before sustaining a calf injury, pulled one back early in the second half and Maxi Gomez headed in the equaliser.
Former Liverpool striker Aspas won Celta the game from the penalty spot after Brais Mendez was fouled with four minutes left and he shed tears of emotion at the final whistle.
(Reporting by Rik Sharma, editing by Ed Osmond)