Canadiens' Christopher Higgins, second from right, celebrates his goal with teammates Roman Hamrlik, left, Andrei Kostitsyn and Tom Kostopoulos in the third period. (LM Otero/Associated Press)

For weeks, the Montreal Canadiens have been unable to stay out of the news, mostly for all the wrong reasons.

For 20 minutes in Dallas on Sunday night, they couldn't stay out of the penalty box, but repeatedly were given a lifeline by a weak Stars power play.

A more disciplined, smarter Canadiens squad took the ice for the second period, quickly grabbed the momentum and never looked back on the way to a 3-1 win.

"That's never the way you want to approach the game," Montreal head coach Guy Carbonneau said of the early glut of penalties. "After we killed the 5-on-3 in the second, that's what we needed. We finally decided not to back down. We kept our composure the last 40 minutes and came up with a big win."

Andrei Kostitsyn, Alex Kovalev and Chris Higgins found the net for the Canadiens, who managed just one goal in losses to Buffalo and Atlanta to start their three-game road trip.

Another positive was the play of all-star goaltender Carey Price. Sporting a 3.71 goals-against average in his previous 15 starts, he kicked aside 31 of 32 shots.

He came up with a big stop on Mike Modano early in the third period and made a glove save on James Neal with 10:32 remaining.

Habs' PK key to victory

Outstanding penalty killing was the key to the victory, Price said.

"When you're going into a 5-on-3, you just want to keep your head," Price said. "I think they only had one shot in that 5-on-3 [to start the second]. When we killed that, that helped us get the momentum. Our guys did a good job on the PK. They blocked a lot of shots and kept everything away from me."

Starting Price ahead of Jaroslav Halak, who has won four straight starts, paid off for Carbonneau.

So, too, did his move to juggle his forward lines as each of the top three units accounted for a goal.

Rookie Max Pacioretty replaced Kostitsyn and skated alongside Tomas Plekanec and Kovalev on the No. 1 line.

Kostitsyn joined Alex Tanguay and captain Saku Koivu, with Higgins dropping to the third unit with Maxim Lapierre and Tom Kostopoulos.

But it took a while for any of the newly formed trios to find a rhythm as the Canadiens totalled 18 penalty minutes in the first period.

Points streak grows

Loui Eriksson made them pay with his team-leading 32nd goal of the season to extend his points streak to five games. The goal came on a 5-on-3 advantage, improving Dallas to 6-for-26 in such situations this season.

Fortunately for Montreal, the Stars failed to connect on their next nine power-play chances — including a stretch of 5-on-3s that lasted about three-and-a-half minutes — and dropped their sixth straight game at home for the first time since February 1970.

"The difference was we could have put the game away in the first," Dallas defenceman Stéphane Robidas said. "We gave the momentum back when they killed all those penalties."

Kostitsyn pulled the Canadiens even at the five-minute mark of the second period, pouncing on a loose puck in the slot and firing it into an open net. The shot was only the fourth of the game for Montreal.

Kovalev pots winner

Kovalev was credited with the eventual winning goal at 14:50. The right-winger's blast from inside the faceoff circle deflected off the left shoulder of Dallas goalie Marty Turco and into the net as time expired on Mike Modano's hooking penalty.

"Our second-period execution was terrible," Stars head coach Dave Tippett said. "It sucked the life out of us."

Higgins put the game away at 5:27 of the third period as his one-timer along the boards found the mark ahead of Turco, who was caught drifting from his net on a shootaround.

With their 35th win of the season and first at Dallas since March 4, 1998, the Canadiens snapped a three-game losing skid and moved in front of Florida into sole possession of fifth place in the NHL's Eastern Conference with 77 points.

The 31-27-8 Stars dropped to ninth in the West, but are tied with seventh-place Edmonton (32-27-6) and No. 8 Nashville (33-29-4) with 70 points.

Montreal will play nine of its next 10 games at home, starting Tuesday against the Oilers at 7:30 p.m. ET.

With files from the Associated Press