Tom Wandell scored twice for Dallas and Loui Eriksson and Eric Nystrom also tallied for the Stars. Kari Lehtonen stopped 28 of 29 shots for the Stars, who have outscored their opponents 10-2 during the streak.
The win pushed the Stars two points ahead of Calgary and Los Angeles in the race for the eighth and final playoff spot in the Western Conference.
The Stars won the second game of a back-to-back for the first time this season. The three-game winning streak was their first since December 10-15.
Minnesota had a two-game winning streak snapped and fell five points out of the eighth and final playoff spot.
The Stars lost defenseman Philip Larsen during the game. He was hit in the head with a puck late in the second period and did not return.
The Stars struck first at 8:48 into the game. Tom Wandell dug a puck out behind the Minnesota goal, put a puck on net and then scored off a rebound to give the Stars a 1-0 lead.
Less than a minute later, Stars goalie Kari Lehtonen made a scrambling save of a Devin Setoguchi redirection to keep it a 1-0 game.
Just 23 seconds after the Stars killed off the first power play of the game, the Stars scored to make it a 2-0 game. Michael Ryder sent a pass cross-ice pass to Loui Eriksson, who put the puck into the open side of the net for 20th goal of the season.
The Stars made it a 3-0 game at 3:53 of the second when Radek Dvorak centered a puck from behind the goal line and Eric Nystrom banged it home from the left circle. That ended the night for Wild goalie Niklas Backstrom, who was pulled after allowing three goals on 14 shots. Matt Hackett took over in net for Minnesota.
Both teams were 0-2 on the power play in the period.
The Stars lost defenseman Philip Larsen late in the period when he was hit in the head on a shot by Wild forward Matt Cullen. His status was not known at the end of the period.
The Stars got in some penalty trouble just after the midway point of the period. Steve Ott took an unsportsmanlike conduct minor and that was followed by a bench minor for abuse of officials, giving the Wild a 40 second five-on-three. They cashed in on that one when Setoguchi scored off a one-timer with 7:17 remaining to make it a 3-1 game.
Sheldon Souray then took a cross-checking minor, giving the Wild a 16 second five-on-three, but the Stars were able to kill that off and preserve the two-goal lead.
Tom Wandell scored into an empty net with 52.3 seconds left to make it a 4-1 final score.
Injured: Dowell (finger), Morrow (neck/shoulder)