It took six rounds of the tiebreaker to settle this one, and Kesler ended it with a backhander past goalie Marty Turco. Stu Barnes had an opportunity to send it into another round but his effort was stopped by Roberto Luongo.
Vancouver scored twice on six opportunities in the shootout with Brendan Morrison also beating Turco, 3-1 this season in the tiebreaker and 15-2 in his career. Jussi Jokinen was the only Dallas player to score on Luongo.
The Stars nearly won the game in overtime when they had several good scoring chances in the final minute.
Mattias Ohlund scored a power-play goal in regulation for Vancouver. Loui Eriksson replied for Dallas.