Boyes ended the game in the bottom of the second round when he deked to his backhand and slid the puck between the legs of Wild goalie Josh Harding. Tim Thomas stopped Zach Parise and Mikko Koivu in the shootout after making 31 saves in regulation and overtime.
Aleksander Barkov scored at 6:49 of the third period to tie the score at 1-1 and help the Panthers (3-6-0) snap their second three-game losing streak of the season.
Jonas Brodin scored a power-play goal in the second period for Minnesota and Harding made 21 saves. Harding came into the game with the best goals-against average in the NHL at 1.15.
This was the first Panthers game this season to go past regulation. Minnesota is 0-2 in shootouts and has lost its overtime game.
The loss wrapped up a 1-2-1 road trip for the Wild, who will host Florida on Nov. 15 in St. Paul, Minn.
Each team had one great scoring opportunity in overtime. Florida's Tomas Fleischmann fired a one-timer from close range that was gloved by Harding with 1:12 left. With the five-minute extra period winding down, Parise redirected Koivu's pass, but Thomas made a sliding pad save.
Minnesota failed to score with a 5-on-3 advantage for 1:19 midway through the third period, and the Wild's Mikael Granlund hit the post with a wrist shot with about 3:30 left in regulation.
Barkov, the second player taken in the 2013 NHL Draft, scored Florida's first power-play goal in four games. He was in the slot when he deflected Fleischmann's one-timer from the top of the right circle past Harding.
Brodin opened the scoring at 4:05 of the second period with Fleischmann in the penalty box for hooking.
Seconds after Thomas dove to his left to stop a rebound by Granlund, the puck slide back to the high slot when Brodin fired a one-timer. The shot went off the stick of Panthers forward Jesse Winchester and went through the legs of Thomas.
The goal was the third of the season for Brodin, the most among NHL defensemen. It also was his ninth point of the season after he had 11 in 45 games as a rookie in 2012-13.
Dany Heatley assisted on Brodin's goal, only his second point in nine games this season. He is still looking for his first goal, matching the longest drought of his career.
The Panthers had a great scoring opportunity five minutes into the game when Kris Versteeg had a breakaway, but Harding stopped his attempt at going through the five-hole after a backhand-to-forehand move.
Each team had a brief 5-on-3 opportunity in the first period, with Minnesota getting the better scoring chances. Jared Spurgeon hit the post on a shot from the side of the net, and Thomas came up strong on shots by Parise twice and on a one-timer by Jason Pominville.