Scott Gomez had a goal and an assist, while Jaroslav Spacek had two assists and drew the game-changing penalty. The Northeast Division leaders snapped a two-game losing streak and had lost five of six.
Carey Price stopped 22 shots — including all 10 he saw in the third period — for Montreal, which took control during the 5-minute power play awarded following Erik Cole's major boarding penalty and held on to snap a four-game road losing streak.
Cole and Chad LaRose scored and Cam Ward made 26 saves for Carolina, which has lost two straight since winning a season-best four in a row.
Momentum clearly swung on the penalty issued to Cole for sending Spacek into the boards near the teams' benches with 4:34 left in the second period — 9 seconds after Cole scored to put Carolina up 2-1.
The Canadiens took full advantage. Kostitsyn tied it at 2 with 3:03 left when he scored from point-blank range, tapping in a feed from Tomas Plekanec.
Picard then put Montreal up with a wrist shot from between the circles that got through traffic and beat Ward for his third goal. Picard skated in nine games late last season for the Hurricanes, who acquired him from Ottawa in February but allowed him to leave via free agency in the offseason.
Cole gave Carolina a short-lived lead with 4:43 left in the period when he scored off a draw, charging toward Price and pushing in his rebound for his 14th career goal against the Canadiens.
The Hurricanes took a 1-0 lead barely a minute into the second period when LaRose scored his seventh career short-handed goal. Gomez tied it roughly 4 minutes later when he took a feed from Hamrlik, split a pair of defenders and beat Ward for his fifth goal.
NOTES: Plekanec has five points in two games against Carolina this season. ... LaRose's goal was his first since a four-point night Nov. 17 against Ottawa. ... Kostitsyn was back in the Canadiens' lineup after a one-game benching. Montreal scratched LW Benoit Pouliot and D P.K. Subban. ... Ward played in the 300th game of his career.