Glen Metropolit scored the go-ahead goal early in the third period after Price caused a reckless turnover and Boston went on to beat the Montreal Canadiens 5-1 Thursday night to avoid elimination in their first-round series.
Tim Thomas stopped 31 shots for the Bruins, who now trail the Eastern Conference quarterfinal 3-2.
"That's the kind of team we are," Metropolit said. "We're not a flashy bunch of guys."
Price gloved a puck at the side of his net and dropped it in front of him, but Petteri Nokelainen got his stick on it before Montreal's Maxim Lapierre and Metropolit batted the puck into an open net 3:31 into the third to put the Bruins up 2-1.
Zdeno Chara scored Boston's second power-play goal of the game at 5:49.
Marco Sturm increased the lead to 4-1 with a short-handed goal at 15:13 when he drove a slap shot past Price into the top right corner and Vladimir Sobotka added an unassisted effort at 17:48.
Phil Kessel returned to the Bruins' lineup and tied it at 1 in the second with his first career playoff goal.
Montreal's Alex Kovalev had a highlight reel goal midway through the first. Game 6 is Saturday night in Boston, where the Bruins will try to extend their season again.
"We knew what we were facing," Chara said.
Kovalev lost his helmet early in the play that led to his goal when he was checked by Chara in front of the Bruins' bench. The high-scoring Russian came away with the puck with his blond locks flowing freely as he gained the Bruins' zone before passing back to defenseman Roman Hamrlik.
Kovalev cut back towards the net and caught Patrice Brisebois' point shot out of midair and dropped it to his feet as he continued across the slot before putting a backhand past Thomas.
Kessel returned to the lineup and got his first career playoff goal on a power play 7:45 into the second. A healthy scratch in the previous three games, Kessel beat Price with a shot from the left side 20 seconds after Hamrlik was sent off for holding.
Boston got a lucky break in the dying seconds of the period that nearly led to a goal.
Price tried to clear a loose puck by pushing it forward but it caromed off Bruins center David Krejci and back towards the net, striking the right post before dropping into the goalmouth behind the Montreal goalie.
Price spun around and swatted the puck away with his stick before Milan Lucic could reach it.
Notes: Bruins D Aaron Ward didn't play because of a knee injury. ... C Kyle Chipchura, RW Matt D'Agostini and G Yann Danis were among six players Montreal recalled from Hamilton of the AHL earlier in the day, along with F Brock Trotter and Ds Mathieu Carle and Pavel Valentenko. F Ben Maxwell also joined the Canadiens from Kootenay of the WHL.