Price stopped all 14 shots he faced in the third period and was perfect on the Tampa Bay Lightning's three attempts in the tiebreaker Saturday night, giving the Canadiens a 2-1 victory.
Lars Eller, Montreal's first shooter, went backhand to forehand before beating Ben Bishop through the pads. Price stopped all three Tampa Bay shooters, ending the game by denying Teddy Purcell's forehand with his pads.
Montreal coach Michel Therrien credited his goaltender for the win.
"He's been phenomenal," Therrien said. "In the third period, when they gave us a push, he was making key saves. He showed again tonight he is one of the best goalies in the NHL."
It was Price's 18th victory of the season but his first in three shootouts. One of the two losses came against the Lightning on Nov. 12 at Bell Centre, when Tampa Bay won 2-1 in a tiebreaker.
All of the scoring took place in a span of less than 6 1/2 minutes in the second period. Tomas Plekanec gave Montreal the lead when he scored at 5:15. Martin St. Louis got Tampa Bay even with his 17th goal at 11:43.
Both teams were coming off a four-game Christmas break and needed a little time to get their legs moving.
"It wasn't easy after the layoff," Plekanec said. "But we put a pretty good effort and we're happy with the win. They pushed hard."
But not as hard as the Canadiens, who withstood a 14-6 shot differential in the third period as the Lightning pushed for the win in regulation.
"I really appreciated our team effort," Therrien said." The energy was there right from the get-go. ... This was a good team effort. Guys competed hard, they were quick on puck, and we didn't force plays when we didn't have to."
Price finished with 23 saves. Bishop stopped 20 shots.
"It stinks not winning the shootout," Lightning coach Jon Cooper said after the sixth straight one-goal game between the Atlantic Division rivals. "You get greedy. Every time you go on one you want to win the thing but their goalie made some great saves. If you want to be in the conversation in March and April, you have to find a way to win the one-goal games and you have to find a way to win the third period."
After a scoreless first period in which the Canadiens (23-13-3) outshot the Lightning 7-3, Plekanec put Montreal ahead when he broke in on Bishop, fought off Alex Killorn's check and flipped the puck past Bishop for his 13th of the season.
St. Louis tied the game when he one-timed a pass from Tyler Johnson past Price from between the faceoff circles. The Lightning captain has points in six straight games.
The win pulled Montreal to within one point of the Lightning in the Atlantic Division. Tampa Bay (23-11-4) hosts the New York Rangers on Sunday night. The Rangers had the night off after a 3-2 road loss to the Washington Capitals on Friday.
"We did leave one [point] on the table and this is a team we are battling with in the division, so it makes tomorrow night all the more important," Cooper said." It will be tough for us with the quick turnaround. [The Rangers] are probably resting in the hotel right now. We will have to find a way."