Stu Barnes added his ninth goal of the season with 3:03 left to stretch Dallas' lead to 4-2. Stephane Boucher and Mike Modano also scored for the Stars, who are 6-2-1 in their last nine games.
Antti Miettinen and Jussi Jokinen had two assists each for Dallas.
Rookie goalie Mike Smith stopped all 15 shots he faced after taking over for starter Marty Turco, who gave up two goals on seven shots in the first period.
With the score tied 2-2 and Minnesota's Mark Parrish in the penalty box for hooking, Zubov's shot from just inside the blue-line eluded goalie Niklas Backstrom for his ninth goal of the season.
Dallas has 66 points, four better than Minnesota in the Western Conference playoff race.
Backstrom made 31 saves and Petteri Nummelin and Pascal Dupuis scored for Minnesota, which had won seven of its previous eight on the road.
All-star left wing Brian Rolston was scratched for the Wild due to a stomach virus.
Rolston, who has a team-high 25 goals and 46 points, had played in Minnesota's first 54 games this season.
Also out for Minnesota was No. 1 goalie Manny Fernandez, the former Dallas backup who will be unavailable for three more weeks because of a knee injury.
Backstrom, a 29-year-old rookie, has played well in place of Fernandez, winning his previous three starts entering Tuesday night.
The Wild got off to a fast start, grabbing a 2-0 lead in the first eight-plus minutes and driving Turco to the bench.
Nummelin got the first goal at 7:27, his third. Dupuis made it 2-0 at 8:08 on a dump-in from beyond the left circle, his 10th.
Turco reacted late on Dupuis' shot, and Stars coach Dave Tippett sent Smith into the game.
Dallas trimmed the deficit to 2-1 at 12:02 of the first period on Boucher's 15th of the season, a shot from the slot off a behind-the-net pass from Jokinen.
Boucher missed the previous two games with a lower-body injury.
Modano's rebound, his 11th goal of the season and 496th of his career, pulled the Stars even at 2 at 12:25 of the second period.
Modano is six goals shy of matching Joe Mullen for the most goals by a U.S.-born player in NHL history.
The goal was Modano's first since Dec. 4. Modano missed 23 straight games because of a hip injury and has been in four games since his return.
Notes: The Stars remain without forwards Brenden Morrow (wrist), Matthew Barnaby (concussion) and Steve Ott (ankle). ... The Wild nearly had a goal in the game's first five minutes on a shot by Pierre-Marc Bouchard but replays showed that Stars C Patrik Stefan was able to stop the puck with his stick just before it crossed the goal line. ... Dallas dominated the second period with a 16-6 shots advantage. ... Turco started his 22nd consecutive game.