Cal Clutterbuck also scored to help Minnesota finish 3-1-1 on a five-game homestand.
Havlat scored at 4:20 of the third period, taking a pass from Matt Cullen, kicking the puck to his stick and sneaking a shot past Kiprusoff to make it 2-1.
Havlat, who scored 18 goals last season for the Wild and 29 goals in 2008-09 for Chicago, hadn't scored since March 29 — a stretch of 18 games. The winner also came a little more than a week after his agent Allan Walsh publicly criticized Wild coach Todd Richards for his use of Havlat.
Backstrom improved to 6-3-2, making 12 third-period saves. With just more than 2 minutes to play, Backstrom made a nice save on a shot that was tipped in the slot by Calgary's David Moss.
While Kiprusoff has more victories against the Wild than any other goalie, Minnesota has won six of seven against the Flames since the beginning of the 2009-10 season.
Bourque opened the scoring for Calgary at 10:45 of the first period. His shot from on top of the right circle beat Backstrom over the shoulder. Since missing two games with an upper-body injury believed to be a concussion, Bourque has seven goals and three assists in nine games.
Clutterbuck tied it with 4:30 left in the first. After Minnesota's Justin Falk held the puck in the offensive zone, the Wild's Andrew Brunette found Clutterbuck just to the right of the goal.
NOTES: The game marked the beginning of a stretch in which the Flames will play nine of 11 games on the road. ... Calgary forward Tim Jackman, who grew up in the Minneapolis suburbs, got into a first-period fight with the Brad Staubitz. ... Forwards Cody Almond and Matt Kassian made their NHL debuts for Minnesota after being called up from Houston of the American Hockey League.