The 23-year-old Spain youth international, a product of Villarreal's academy, was unable to prevent Gomez levelling with a clinical finish from a tight angle in the 65th minute.
Substitute Oscar De Marcos fired Bilbao ahead with a close-range header 10 minutes later before Gomez completed his double in the 82nd with another low strike and Ander Herrera nodded a fourth with four minutes to go.
Valladolid substitute Valdet Rama then lashed the ball into the roof of the net in added time after a powerful run through the home defence.
Bilbao, who visit Atletico Madrid in the quarter-finals of the King's Cup on Thursday, have won nine of their 11 league games at their new stadium this season and drawn two.
Monday's victory lifted them back above Villarreal, who won 2-0 at home to Almeria on Sunday, into the fourth spot that earns a berth in Champions League qualifying next season.
The Basque club have 39 points from 20 matches and Villarreal are fifth on 37. Real Sociedad, who drew 2-2 at Getafe on Sunday, are sixth on 33 while Valladolid are third from bottom on 16.
"We are on a very good run at home," Gomez told television broadcaster Cuatro. "We have often fallen behind but managed to turn the game around and that counts for a lot.
"The team is in good shape and we are maintaining our intensity for the whole 90 minutes which is very important."
Elsewhere, third-placed Real Madrid closed within a point of joint leaders Barcelona and Atletico Madrid thanks to Saturday's 5-0 win at bottom club Real Betis.
On Sunday, Barca came from a goal down to draw 1-1 at Levante and Atletico let slip the lead in a 1-1 stalemate at home to Sevilla.
Barca and Atletico have 51 points, with the champions ahead on goal difference.
(Reporting by Iain Rogers editing by Tony Jimenez)
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