Ibai Gomez scored twice in what ultimately proved to be a comfortable run-out for Athletic in the Basque Country, once Marino's resolve had been broken and the early setback of an Oscar goal overcome.
Oscar De Marcos and Ander Herrera heaped further misery on 18th-placed Valladolid, who would score again late on through Valdet Rama, while Bilbao used the three points to leapfrog Villarreal and reach fourth place in the table.
Athletic put six goals past Almeria last time out at San Mames and fancied their chances of dishing out similar punishment to La Liga strugglers Valladolid.
Only four minutes had been played when Herrera streaked into the box to get a fierce shot away, but Marino pulled off an unlikely save to give Valladolid an early confidence boost.
They survived another near miss, Aymeric Laporte heading just over the crossbar, before Oscar opened the scoring against the run of play in the 15th minute.
The veteran midfielder notched the first goal of his second spell at the club by turning the ball home from six yards.
Aritz Aduriz soon burst into the area in search of an equaliser only for Marino to show quick reflexes to deny the Basque and preserve his side's surprise lead.
The Spain Under-23 keeper was even more impressive when defusing a Gomez rocket and Valladolid would take their slender advantage into the break.
To prove his first-half performance had been no accident, Marino set about amazing the San Mames crowd with a succession of fine saves following the restart.
He parried Gomez's sweetly-struck effort to safety before blocking Aduriz at close quarters and snaffling Herrera's long-range sighter - all in a frantic four-minute period.
The pressure abated and Marino was afforded some valuable time to compose himself and prepare for the next raid, which came in the 65th minute.
But this time, despite his best efforts, he could not keep Athletic at bay and watched helplessly as Gomez swept the loose ball home after he thought had parried Aduriz's shot clear.
Ten minutes later, Bilbao turned the game on its head and began to pick all of Marino's good work apart.
Aduriz was once again heavily involved as he nodded across a crowded Valladolid box for De Marcos to finish the job with his own head.
There was a sense of inevitability in the air by this point and, with eight minutes remaining, Athletic's third goal arrived through a familiar source as Gomez tucked away Aduriz's neat pass from the left.
Herrera then made it 4-1 from De Marcos' cross in the 86th minute and although it offered the visiting faithful some reason to be cheerful, Rama's stoppage-time response for Valladolid was merely a consolation goal.