Norman landed awkwardly on his head right before half time, ending his night, after star recruit and halfback Kieran Foran was a pre-game withdrawal.
The Broncos took a little while to get going but never looked like conceding the game even before Norman was injured, which happened with Brisbane up 14-4.
For the visitors, winger Corey Oates was heavily involved, scoring one try and setting up another, while both halves Ben Hunt and Anthony Milford worked their way into the match well.