Officials ruled the Devils were entitled to a penalty shot with 50 seconds left after Montreal defenseman Josh Gorges closed his hand on the puck while in the crease.
Zach Parise skated in and fired on Price but couldn't dent him for the equalizer, and the Canadiens held on during the final seconds to notch only their second win in nine games.
Price finished with 28 saves to earn the victory.
Nick Palmieri netted the Devils' only goal and Martin Brodeur made 22 saves in the loss.
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