Reilly Smith, Cody Eakin and Antoine Roussel also scored for the Stars, who overcame a 3-1 deficit to win for the fifth time in six games. Backup goalie Richard Bachman rebounded from a rough start and earned the victory in relief of injured Kari Lehtonen.
Daniel Sedin, Chris Higgins and Alex Burrows had goals for the Canucks, and captain Henrik Sedin became the club's career scoring leader.
Dillon, a 22-year-old native of the Vancouver suburb of Surrey, B.C., was playing his first NHL game in his hometown. He gave Dallas the lead for the first time when he slid behind coverage from his defensive position and fired in Jamie Benn's cross-ice pass.
Dallas outshot Vancouver 29-28. The Stars were blanked on four power plays, while the Canucks could not convert on three.
After allowing three goals on the first six shots he faced, Bachman stopped 15 straight shots to finish with 21 saves.
Henrik Sedin became Vancouver's career scoring leader by getting two assists to surpass former teammate Markus Naslund. Sedin now has 757 points, one more than Naslund. The former teammates hail from the same hometown of Ornskoldsvik, Sweden.
Vancouver's Ryan Kesler played his first game since last spring's playoffs after recovering from shoulder and wrist surgery. Kesler drew a loud cheer as he came out to take a faceoff on his first shift. He quickly made an impact by drawing an interference penalty on Dillon just 1:16 into the game.
But the Canucks could not capitalize on the power play, in part because a wide-open Kesler fanned on a one-timer of Henrik Sedin's cross-ice pass. Kesler had another chance around the 5-minute mark, but Lehtonen stopped him as he attempted a backhand while coming around the net.
Kesler had another excellent chance during another power play midway through the first period, but the puck hit Lehtonen's blocker and the crossbar and bounced away. Lehtonen came up big a little while later as he got the shaft of his stick on Jordan Schroeder's wrist shot that appeared headed for the top corner of the net.
But Lehtonen left the game moments later during a TV timeout and was replaced by Bachman. Mason Raymond scored on the first shot Bachman faced as he stuffed in a pass from Jannik Hansen, but the goal was disallowed because of incidental contact.
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Only 11 seconds later, Smith beat Vancouver goalie Cory Schneider from a sharp angle.
Daniel Sedin drew the Canucks even 3:21 into the second period when he roofed in a backhand from along the goal line as his twin brother Henrik passed the puck from behind the net.
Higgins gave the Canucks a 2-1 lead 53 seconds later as he fired home a shot from the high slot for his third goal of the season. Kesler earned his first point of the season as he drew the second assist on the play.
Henrik Sedin took sole possession of Vancouver's points record midway through the second when he sent a cross-ice pass to Alex Burrows, who made no mistake as he one-timed the puck behind Bachman.
After Henrik Sedin broke the record, the crowd gave him an extended standing ovation
-- even while he sat on the bench, then back on the ice and during a TV timeout. During the break, the Canucks aired a video saluting him, with Naslund offering his congratulations.
Henrik Sedin responded by raising his stick and clapping in support of the crowd.
Eakin brought Dallas within a goal at 17:50 of the middle period, jamming in the puck after it trickled down Schneider as he tried to squeeze Trevor Daley's shot.
Roussel tied it for the Stars at 12:22 of the third period when he stuffed in a loose puck during a scramble.
NOTES: Three fights occurred 3 seconds apart in the second period. In the middle bout, former Ivy League teammates Aaron Volpatti of Vancouver and Ryan Garbutt of Dallas squared off. Volpatti and Garbutt played together during three seasons at Brown. ... Dallas wing Ray Whitney, 40, sat out his seventh straight game with a foot injury. ... Stars forward Jaromir Jagr turned 41. ... Canucks defensemen Andrew Alberts and Cam Barker were scratched for the 13th straight game. They have yet to play this season. Vancouver forward Andrew Ebbett was also scratched. ... It was the first of three meetings between Dallas and Vancouver this season. ... Stars defenseman Aaron Rome played his first game against his former team since leaving last summer as a free agent.
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