Mowbray believes the 22-year-old has silenced his doubters after coming under fire from a small section of fans.
The Boro chief has kept faith with the England Under-21 international and he was handed the man-of-the-match award following last weekend's win at Watford.
And Mowbray expects the Boro Academy graduate to remain a regular for years to come.
"Jason's form has been magnificent all season. In my time here I've heard the murmurings but you've got to give young goalkeepers opportunities to play," he told the Evening Gazette.
"I think he's doing exceptionally well. He's a big, big talent and his personality's great for the job and he's going to be very important for us."