Price was the fifth overall pick in the 2005 NHL draft by the Montreal Canadiens and signed a contract with the club last week. He was assigned him to the Bulldogs for the final weekend of the regular season and was given the start in the playoff opener.
He went 1-1 in two starts last weekend, including a 2-1 loss at Rochester on Sunday.
The Bulldogs broke a scoreless tie early in the second period on a disputed goal by Zach Stortini.
Rochester argued that goalie Craig Anderson had the puck covered, but Stortini and Matt D'Agostini kept it alive during the goal-mouth scramble in the opinion of referee Dean Morton.
Maxim Lapierre scored into an empty net with 8.8 seconds to play.