Despite firing 39 shots on net and getting multiple scoring chances late in the game, Vancouver couldn't quite break Dallas' domination.
Alexander Radulov scored the overtime winner and the Stars snapped the Canucks' four-game win streak with a 2-1 victory on Monday night.
The Stars now own a 13-0-1 record against Vancouver in their last 14 meetings. But on multiple occasions Monday night, it looked as though the Canucks would emerge triumphant in the tightly contested game.
"I thought we played really well," said Sam Gagner, who scored his first goal for the Canucks on a power play to tie it in the third. "If we scored on that 2-on-1 in overtime or some of our chances in the third, it's obviously a different story.
"If we play like that most nights in this league you win. We have to keep playing that way. We're going in the right direction and playing good hockey."
Jacob Markstrom made 27 saves for the Canucks (6-3-2) and was especially impressive in the first and third period. It was his first start after watching the past two games from the bench while Anders Nilsson got the call.
"It was a really good game, but you want to win hockey games," said Markstrom. "I hate losing."
Tyler Seguin found the back of the net in regulation for Dallas (7-5-0), which improved to 3-1 on its current five-game road trip that finishes up Thursday in Winnipeg.
Ben Bishop made 38 saves for the Stars.
Radulov won it in overtime when he carried the puck the length of the ice and fired a bullet over the blocker-side shoulder of Markstrom at 2:28. He has been red-hot as of late with three goals and six points in his last three games.
"He's a wild-card player," said Stars head coach Ken Hitchcock. "He's going to do things on the ice that are creative and you are going to have to live with it, but he competes on the puck and that's a big part of it. He's a very competitive player and I think he elevates the rest of our competitiveness."
Seguin opened the scoring in the second with Canucks forward Thomas Vanek in the penalty box for the second time in the first three minutes of the period.
Seguin one-timed his seventh goal of the season with an Ovechkin-like shot while down on one knee at 3:11. The goal broke Vancouver's streak of 14 consecutive penalties killed.
"It was a great shot, he put it right in the corner, only a couple guys can do that and he's one of them," said Bishop.
The Canucks tied the game six minutes into the third while on the power play. After Markstrom chased down a puck to diffuse a short-handed breakaway, Vanek took a quick pass from Daniel Sedin in the slot at the other end and fired a hard shot that rebounded to Gagner. The centre slotted his first goal as a Canuck at 13:51, sending the crowd into a frenzy.
"We were in a battle, we were in a dog fight," said Canucks coach Travis Green. "That was a great hockey game. I thought they played a hell of a game on the road; I thought we played a hell of a game at home. I liked the way our team stuck with it."
Notes: The Canucks were without rookie winger Brock Boeser, who injured his foot blocking a shot in a 6-2 win over Washington. Vancouver called up forwards Jayson Megna and Anton Rodin from Utica of the AHL. ... Dallas were without Martin Hanzal (lower body) and Stephen Johns (concussion).