Bilbao almost levelled things up within six minutes when Aritz Aduriz turned a low cross towards goal, only to be denied by a smart save from Marino.
The Valladolid keeper was called into action again shortly afterwards, almost gifting the hosts a goal when he spilled Herrera's effort before recovering in time to collect it at the second attempt.
Ibai was the next to test Marino, doing so five minutes after the restart with a curling effort from just inside the box that drew a fine stop from the visiting keeper.
Marino was finally beaten in the 65th minute when his loose save was pounced on by Ibai, who slotted the ball into the bottom corner to level things up.
The hosts completed the comeback 10 minutes later when Oscar De Marcos rose in the area to nod home a cross from close range.
Bilbao made sure of all three points with a third goal in the 82nd minute as Ibai danced into the box before sliding a shot past the keeper and into the bottom corner for his second goal of the night.
The hosts then capped off a fine second-half performance by extending their lead even further with just three minutes of normal time remaining when Herrera nodded De Marcos's cross home from close range.
There was still time for Valladolid to get a consolation goal through Valdet Rama, but it was too little too late for the visitors, who remain in the bottom three.