Mikael Backlund scored the overtime winner at 2:25 of the extra frame from Sean Monahan and Mark Giordano. Backlund's first goal of the hockey game was shorthanded and came at the one minute mark of the third period to put the Flames up 3-1 at the time.
Calgary's two goal third period lead evaporated however when Dany Heatley and Keith Ballard scored for Minnesota to force overtime.
Backlund was one of four Flames to record a multi-point game in the contest. T.J. Galiardi had a goal and an assist and defensemen Mark Giordano and Chris Butler had two assists each.
The Flames with the win improve to 21-27-7 but are still 14 points back of the Vancouver Canucks for a playoff spot in the Western Conference.
This was the Flames' last home game before the 2014 Olympic Winter Games. Calgary now goes on the road for three straight games starting in Montreal on Tuesday.