Campbell pounced for his third goal in three games after Richard Garcia had fired Hull in front at the start of the second half, to leave dreadful Wolves without a win in five games.
Campbell has now scored six goals since arriving at the club from Manchester United in October, and Brown is desperate to tie up the services of the youngster for the remainder of the campaign.
"Anybody who scores goals is an important asset," said Brown. "His sort of goal strike-rate would be appreciated in any division.
"He is on loan until the middle of January and as far as I'm concerned it is a no-brainer - I'd like to keep him until the end of the season.
"I will try to do as much persuading as possible, but the decision is out of my hands."