DALLAS (AP) -Once the Montreal Canadiens survived their early parade to the penalty box, they knew they had a chance against the Dallas Stars.

Carey Price made 31 saves, and Montreal killed nine of 10 power plays in the Canadiens' 3-1 victory Sunday night.

The Canadiens took nine penalties in the first period, helping the Stars to a 10-3 shots advantage. But Dallas was unable to extend its lead, managing one shot during a stretch of 5-on-3 that lasted about 3 1/2 minutes, and Montreal came back with second-period goals from Andrei Kostitsyn and Alex Kovalev.

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``That's never the way you want to approach the game,' Montreal 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.'

Chris Higgins added a third-period goal to help the Canadiens jump to fifth in the Eastern Conference and improve to 4-12-1 in their last 17 road games.

Montreal will play nine of its next 10 games at home.

``That's why we wanted to win this game,' Carbonneau said. ``We didn't want to come with three losses in a row on this trip. We think this win should give us a lot of confidence.'

Price, 3-10-1 since returning from an ankle injury, came up with a big stop on Mike Modano early in the third and made a glove save on James Neal with 10:32 remaining.

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.'

Loui Eriksson had a power-play goal for Dallas, and Marty Turco made 16 saves. The Stars lost their sixth straight at home to match a franchise record set in 1970 in Minnesota. Dallas has scored seven goals during the six-game home skid.

The Stars were coming off a 2-0-1 trip against Pacific Division rivals San Jose, Los Angeles and Anaheim, but power-play problems contributed to another home loss. Tied for seventh in the West with 70 points, Dallas is 8-for-66 in its last 15 games.

The Stars got the early jump when Eriksson scored his 32nd at 4:52 of the first period. He had an open net after the puck caromed off Montreal defenseman Mike Komisarek's skate while the Stars held a 5-on-3 advantage.

But the Stars could have had more.

``The difference was we could have put the game away in the first,' Dallas defenseman Stephane Robidas said. ``We gave the momentum back when they killed all those penalties.'

Montreal tied it 5 minutes into the second period when Kostitsyn notched his 23rd from the slot off Saku Koivu's setup.

Dallas had just killed a power play when Kovalev blasted a shot from the top of the left circle that whizzed past Turco's left shoulder at 14:51 of the second period for Kovalev's 16th, giving Montreal a 2-1 lead.

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

Notes: Carbonneau and assistant coach Kirk Muller are former Stars players. Montreal GM Bob Gainey is a one-time Dallas coach and GM, and Canadiens assistant coach Doug Jarvis filled the same role for the Stars. Ribeiro, Robidas and Steve Begin are former Montreal players. ... This was the only meeting between the teams this season. Dallas won the last matchup at home on Dec. 23, 2007, 4-1. ... Turco has started 36 of the last 37 games. ... RW Jere Lehtinen missed his third straight game for Dallas with what the club is terming an upper-body injury. ... Montreal's Mathieu Schneider was assessed a double-minor for high-sticking in the first period after his stick struck Ott in the mouth, knocking out one of Ott's front teeth and breaking others. Ott remained in the game. ... Montreal was outscored 7-2 in losing the first two games on its three-game trip.