The Wild won their second straight and picked up two much-needed points in their bid to earn a playoff position. Minnesota began the night five points out of the eighth and final Western Conference post-season berth.
Bergenheim tied the contest with 4:12 left in regulation after Matt Cullen had given Minnesota a 2-1 lead early in the third period with a power-play goal.
The Panthers, who went into the contest tied for the lead with Winnipeg in the Southeast Division, have lost four in a row.
Backstrom made 41 saves while Jose Theodore stopped 26-of-28 shots.