Vancouver No. 1 goalie Roberto Luongo got the game off on the second leg of a back-to-back, and Schneider seemed to be on pace for his fourth career shutout until a misplay in the third period allowed Dallas to get on the board.
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Schneider went behind his net to play the puck, but fanned when he tried to pass. Dallas' Vernon Fiddler tucked the puck into an open net at 7:44 for his eighth goal of the season.
But the Canucks held on to improve their conference-best road record to 23-11-5.
"I felt pretty good playing the puck until that last one," Schneider said. "It was tough to put my team in that position but we didn't crack."
Dallas is eighth in the Western Conference, tied with ninth-place Colorado with 85 points. The Stars entered the night with the Pacific Division lead but dropped a point behind Los Angeles and Phoenix.
Schneider, who boosted his record to 17-7-1, denied Mike Ribeiro's penalty shot at 12:55 of the second period. Ribeiro tried a nifty move he uses in shootouts to get a shot on the backhand, but Schneider stood his ground and easily stopped the puck.
"I wasn't real sure what he was going to do with it, but he got it pretty tight," Schneider said. "I don't know if he was trying to go past my blocker or through my arm, but I was able to stay with it and make the save."
Ribeiro had exited the penalty box, skated in alone on a breakaway and was slashed by Dan Hamhuis, earning the penalty shot.
Vancouver capitalized on its first shot of the night at 4:46 of the opening period when Raymond was wide open to the right of Stars goalie Kari Lehtonen. Raymond netted his ninth goal of the season, converting Henrik Sedin's setup that glanced off the stick of Hamhuis to Raymond.
Kevin Bieksa made it 2-0 at 4:18 of the third period when he tucked a rebound past Lehtonen for his eighth of the season. Sedin and Raymond assisted for the Canucks, who had been slumping at 3-5-3 in their previous 11 games.
The Canucks were without Daniel Sedin, the team leader with 30 goals, sidelined indefinitely because of a head injury. Sedin is back in Vancouver after taking an elbow to the head from Chicago's Duncan Keith in the first period of the Blackhawks' 2-1 overtime win over the Canucks on Wednesday night.
Henrik Sedin spoke to his brother by phone earlier Thursday, telling reporters after the game that Daniel was still feeling the effects of the elbowing.
"He has symptoms, a little bit of a headache, which comes with a hit like that," Henrik said.
Dallas pulled Lehtonen late and had a 6-on-4 advantage when Bieksa was called for high-sticking with 44.9 seconds left, but the Stars never managed a shot on goal.
The Stars had been 11-2-1 over their previous 14 games, but they had few serious scoring chances against Schneider.
Last season, the Stars lost all four games to the Canucks by a total score of 20-5. This season, Dallas won the first two matchups before falling Thursday. The teams have their final regular-season meeting March 30 at Vancouver.
Thursday night's game included plenty of after-the-whistle shoving and talking resulting in a total of 15 minor penalties plus a fight between Dallas' Jake Dowell and Vancouver's Dale Weise.
"We wanted to get involved in an extracurricular game," Stars coach Glen Gulutzan said. "Just some of the exchanges and penalties and the frustration level -- just way too high."
Vancouver was making the third stop on a four-game trip. The Stars played the third of a four-game homestand. ... Dallas will be without D Mark Fistric for at least a week due to a strained abdominal muscle sustained Tuesday night in a shootout win over Phoenix. ... In addition to Daniel Sedin, the Canucks are minus forwards Andrew Ebbett (collarbone), Aaron Volpatti (shoulder) and Steve Pinizotto (shoulder), and D Keith Bullard (concussion). ... Ribeiro is 0 for 3 on career penalty shots.