Colorado beat the first-time NHLer 6:13 into the opening frame, burying a loose puck in the crease to give the visitors the lead.
Captain Gabriel Landeskog doubled the score for the Avalanche six minutes later, in a busy first period for Primeau. The seventh round pick from 2017 faced 14 shots through 20 minutes.
Forward Jesperi Kotkaniemi meanwhile left the game with an upper body injury following his first shift, and would not return.
Near the midway mark of the second period, Colorado forwards J.T. Compher and Matt Calvert took advantage of a shorthanded two-on-one to make it 3-0.
The Habs have allowed three goals this season while on the power play.
Brendan Gallagher got Montreal on the board with 2:18 to go in the middle frame.