Eric Nystrom and Philip Larsen scored for the Stars (24-21-2), who are 1-5-1 the last seven games. Kari Lehtonen, who was pulled after giving up four second-period goals, made 15 saves. Richard Bachman stopped six shots in the third period for the Stars.
Dallas led 2-1 after Larsen scored his first NHL goal at 11:03 of the second period. But Minnesota, which has struggled to score the past six weeks, quickly changed the momentum.
Clutterbuck tied it 2-2 when he picked up a loose puck in the Dallas zone and flipped it over a sprawling Lehtonen. Just 14 seconds later, Rau put the Wild ahead for good by scoring his first career goal in his first NHL game. Rau's shot from the left side of the crease went off the stick of Dallas' Brenden Morrow and into the net.
Brodziak finished off the flurry at 14:36 when he took a perfect pass from Heatley and snapped a shot into the open side of the net. The goal Brodziak's second in 16 games.
The three goals in 59 seconds set a franchise record for the Wild, breaking the mark of three in 1:41, set in 2004. The four goals were also Minnesota's most in a period in more than two years.
Heatley stretched the lead to 5-2 just 89 seconds into the third. Going in on a 2-on-1 break, Heatley passed the puck to Warren Peters before getting it back and beating Bachman. Heatley's three-point game was his first with the Wild and his first since November 2010.
The scoring outburst was a welcome change for the Wild. While Minnesota had the best record in the NHL in early December, they have had offensive troubles lately. Over the previous 17 games, the Wild had managed only 28 goals (1.65 per game). Minnesota scored more than two in a game only three times in that stretch.
The lack of offense was especially glaring during Minnesota's recent four-game road trip. The Wild scored just six goals in those four games, going 0-3-1 and sliding backward in the Western Conference standings.
The five goals for Minnesota tied a season high.
Dallas took a 1-0 lead late in the first period. Nystrom, traded by the Wild to the Stars on Oct. 12, tipped in a shot from Stephane Robidas at 18:38 of the first period.
Setoguchi tied it when his shot at 9:06 of the second sneaked over Lehtonen's shoulder and just under the crossbar.
NOTES: Wild D Marek Zidlicky was a healthy scratch for the first time since being acquired by Minnesota before the 2008-09 season. ... Minnesota C Matt Cullen was honored before the game for having recently played in his 1,000th NHL game. ... Rau, a native of Eden Prairie, Minn., became the sixth Wild player this season to make his NHL debut. ... Dallas, which lost Friday to Tampa Bay, is 0-7-1 in the second-half of back-to-backs this season. ... The game was the finale of Hockey Day in Minnesota, an event featuring televised high school, college and NHL games. ... On Sunday, the Wild will host their annual outdoor public practice at the Oval in suburban Roseville, Minn.