Valeri Nichushkin and Erik Cole scored for Dallas (11-7-2), which was coming off a 7-3 victory over the Calgary Flames on Thursday and extended its road winning streak to six games.
Henrik Sedin scored for Vancouver (11-8-3), which got 21 saves from Roberto Luongo as the Canucks dropped their fourth in a row.
After Lehtonen held the Dallas fort in a second period that saw Vancouver hold a 20-5 edge in shots, Cole made it 2-0 early in the third. Henrik Sedin made a bad decision to step up at the Dallas blue-line while covering for a pinching Kevin Bieksa, resulting in a 2-on-1 the other way that saw Cody Eakin feed Cole for his second of the season at 1:42 of the third.
Henrik Sedin had a goal in the second period controversially waved off, but finally got Vancouver on the scoreboard at 3:06 when he chipped a shot over Lehtonen with the Canucks on the power play for his fourth of the campaign.
Vancouver made a late push, but Lehtonen wasn't really troubled much the rest of the way in recording his 10th win of the season as the Canucks mustered just 10 shots in the final period.
Down 1-0 after the first, Vancouver looked to have tied it at 6:42 of the second when Henrik Sedin beat Lehtonen upstairs from a sharp angle.
The celebrations were short-lived, however, as the goal was waved off for what the officials deemed "incidental interference" by Daniel Sedin on Lehtonen at the top of the crease. Television replays appeared to show no contact between the two players, which left both the crowd at Rogers Arena and Canucks coach John Tortorella incensed.
The Canucks' 28th-ranked power play had another chance on the same man advantage, but Lehtonen made a great stop on Vancouver defenceman Kevin Bieksa.
One of Dallas' few chances of the period came on a 2-on-1 with about eight minutes to go, but Stars forward Jamie Benn was stopped by Luongo.
Canucks forward Alexandre Burrows then redirected a pass from Henrik Sedin that beat Lehtonon but not the post as Vancouver led 33-13 on the shot clock after 40 minutes.
The Stars' top line continued its recent hot streak when Nichuskin opened the scoring at 9:33 of the first period. Benn worked the puck behind the net to Tyler Seguin, who in turn fed the 18-year-old Russian on Luongo's doorstep for his second of the season.
Seguin had four goals and an assist against Calgary on Thursday, Benn finished with a goal and five assists, and Nichuskin picked up two assists.
Vancouver, which was coming off a 2-1 overtime loss to San Jose on Thursday that saw the Canucks give up the tying goal with 65 seconds to go in regulation, nearly grabbed an early lead on a Henrik Sedin breakaway that was stopped by Lehtonen less than a minute in.
The Canucks captain then got too fancy on a 2-on-1 a few minutes later when his unnecessary backhand spin-o-rama pass to Daniel Sedin was intercepted.
Lehtonen then made a good pad stop on Zack Kassian before Nichuskin opened the scoring.
Notes: Seguin now has points in four straight games (six goals, two assists). ... Benn was the first Stars player to record six points in game since Mike Modano had two goals and four assists on Feb. 1, 1995. ... Canucks backup goalie Eddie Lack signed a two-year contract extension with the team on Friday. ... Canucks forward Jannik Hansen returned to the lineup after missing 10 games with an upper-body injury. ... Canucks forward Ryan Kesler and Stars forward Vernon Fiddler both played their 600th career game. ... The Canucks host the Florida Panthers on Tuesday, while the Stars welcome the New York Rangers on Thursday.