Scott Gomez had a goal and an assist, while Spacek had two assists and drew the game-changing penalty -- a 5-minute boarding major on Erik Cole that gave the Canadiens plenty of time with the man advantage.
"Our special teams have always been pretty important for us," goalie Carey Price said. "It won us the game."
Price stopped 22 shots -- including all 10 he saw in the third period -- for Montreal. The Northeast Division leaders, who had lost five of six, fell behind twice before rallying to snap losing streaks of two overall and four on the road.
"It just shows the team we have," Gomez said. "We've got a lot of veteran guys in here and the young guys are playing great. But when you're going bad, sometimes [giving up] that first goal is just, 'Oh, here we go again.' But we've gone through it all. We know how to win. We've just got to put it together."
Momentum clearly swung on the penalty issued to Cole for sending Spacek into the boards near the benches just as the Montreal defenseman turned his back with 4:34 left in the second period -- 9 seconds after Cole scored to put Carolina up 2-1.
Spacek called it "kind of turning point for us." Cole said it was "a terrible play on my part" and admitted that "it cost us the game."
And Carolina coach Paul Maurice compared the call to "arresting a telephone pole after a drunk driver hits it."
"I understand why there's an issue here, but there's no way Spacek doesn't know that hit's coming because Cole's chasing him up the ice," Maurice said. "They aren't going in opposite directions. They're going in the same direction. So he's finishing his hit.
"There's no way Erik Cole knows he's going to turn his face to the glass at the very last second," he added. "There's no invitation, 'Dear sir, I'm going to hit you. Would you mind keeping your shoulders square to me so that I don't get a 5-minute penalty?"
It wound up being the break the Canadiens needed. 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 59.4 seconds left in the period when he unloaded a wrist shot from between the circles that got through traffic and past 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.
"When you sit for 5 [minutes], that's a tough one to kill off," Maurice said.
Cole gave Carolina its short-lived lead with 4:43 left in the second when he scored off a draw, charging toward Price and pushing in his rebound for his 14th career goal against the Canadiens.
All the scoring came in the second period, with the Hurricanes taking a 1-0 lead barely a minute in 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.
"We had good control of the hockey game -- although they scored the two goals, I thought we played well, and we did things that we wanted to do," Montreal coach Jacques Martin said.
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.