Canadiens defenseman Josh Gorges was whistled for covering the puck in the crease with 49.4 seconds remaining and Montreal holding a tenuous 2-1 lead.
Parise came up slowly on the penalty shot, and his backhand stayed on the ice, allowing Price to kick save the attempt with his left leg.
"I was just trying to go five-hole and I missed my shot," a frustrated Parise said. "I didn't get it back across far enough, so it was kind of an easy save for him."
Price stood tall in the remaining time and totaled 28 saves in the win, Montreal's second in its last eight games. Erik Cole scored the eventual game- winner and assisted on Max Pacioretty's second-period tally.