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However, the draw could affect their battle with Atlético Madrid for third place. Villarreal now have 55 points, just one ahead of Atlético, who could overtake them if they defeat Getafe on Saturday.
For their part, Alavés moved up to 28 points in 16th place, three points clear of the relegation zone.
Villarreal looked set to leave empty-handed after their defender Rafa Marín inadvertently gave the hosts the lead with an own goal in the 40th minute.
But Ivorian forward Nicolas Pépé rescued a point for the visitors with a dramatic equaliser eight minutes into stoppage time.
The round continues on Saturday with Girona facing Athletic Bilbao, Real Oviedo hosting Valencia, and Real Madrid Castilla taking on Elche.
On Sunday, Mallorca will play Espanyol, league leaders Barcelona face Sevilla, Real Betis meet Celta Vigo, and Real Sociedad take on Osasuna.
The round concludes on Monday with Rayo Vallecano hosting Levante.