Mikko Koivu beat Craig Anderson with wrist shot in the high slot to break a 3-3 tie with two minutes and 57 seconds remaining in the game.
The Wild captain’s goal came eight minutes and six seconds after the Senators tied the game with a power play goal.
The Wild turned the game around in the second period with a pair of goals to turn a deficit into a lead.
Jonas Brodin beat Anderson with a wrist shot from the point through traffic to start the Wild’s initial rally.
Dany Heatley gave the Wild their first lead of the game at the 6:15 mark of the second period. He banged a loose puck at the side of the net under Anderson.
The Senators (8-9-4) got on the board first with a shorthanded goal by Kyle Turris just less than six minutes into the game.
Jason Pominville quickly answered with a goal on the same power play 59 seconds later off a backdoor pass from Zach Parise.
The Wild (14-4-4) return to action Saturday against the Winnipeg Jets at the MTS Centre.
No. 3 - Jonas Brodin. The Wild defenseman recorded a goal and an assist.
No. 2 - Dany Heatley. The Wild forward recorded a goal and an assist.
No. 1 - Mikko Koivu. The Wild forward recorded a goal and two assists.
Minnesota…..1 2 1 - 4
Ottawa…..…..2 0 1 - 3
First Period - 1, Ottawa, Turris 6 (MacArthur), 5:54 (sh). 2, Minnesota, Pominville 13 (Parise, Koivu), 6:53 (pp). 3, Ottawa, Zibanejad 5 (Grant, Condra), 11:11. Penalties - Cowen, OTT (interference), 5:36.
Second Period - 4, Minnesota, Brodin 4 (Heatley Fontaine), 3:00. 5, Minnesota, Heatley 4 (Koivu, Brodin), 6:15. Penalties - Brodziak, MIN (roughing), 3:46; Borowiecki, OTT (roughing), 3:46; Stoner, MIN, major (fighting), 6:23; Neil, OTT, major (fighting), 6:23; Borowiecki, OTT (boarding), 7:06; Grant, OTT (high sticking), 18:36.
Third Period - 6, Ottawa, Michalek 4 (Zibanejad, Karlsson) 8:57 (pp). 7, Minnesota, Koivu 5 (Parise, Coyle), 17:03. Penalties - Heatley, MIN (hooking), 3:11; Pominville, MIN (hooking), 8:39.
Shots on goal - Minnesota 6-10-9 25. Ottawa 18-12-7 37.
Goalies - Minnesota, Harding (34-37). Ottawa, Anderson (21-25). Referees - Francois Charron, Brian Pochmara. Linesmen - Derek Nansen, Tony Sericolo.