Vale's pressure told in the 42nd minute when Bradford left-back James Meredith scuffed an intended backpass and Hughes nipped in to round Jon McLaughlin and slot the ball into an unguarded net.
The visitors equalised in the 59th minute after a brilliant piece of skill by Nahki Wells, who fired in the loose ball from two yards after his initial effort was saved.
But Vale's winner arrived seven minutes later when Doug Loft struck a deflected 20-yard shot from Hughes' perfect lay-off.
Adams, who handed Hughes his first start of the campaign, said: "I wanted a big man to lead us and what a fantastic performance he gave. He epitomised everything we did.
"There are things in his past which I can't deal with and he's had to deal with, but I can only say he has been first class since the first day he walked through the door at this football club.
"But it was a terrific team effort all round and I'm absolutely delighted. I questioned my players' enthusiasm for the game after we lost at Colchester last week, but no-one could question them here.
"From the off they were at it and their effort and commitment to help each other was first class. They stuck their bodies on the line and I couldn't have asked for a better response.
"Bradford are a good side and we had to withstand a bit of pressure in the second half, but we could have been three or four goals up at half-time.
"The performance at Colchester shocked me because I know I've got some very good professionals in the dressing room, but the reaction they gave was outstanding."