The Wild also accumulated a season-high 38 penalty minutes -- 20 of those going to Matt Kassian, who won two fights against Darcy Hordichuk after being called up from the AHL earlier in the day.
"I love emotion in our game, and we had emotion right down the line," coach Mike Yeo said.
Backstrom will likely make a second straight start on New Year's Eve after making 27 saves and getting into a scrap with Oilers forward Ryan Smyth as Thursday's contest ended.
Phoenix coach Dave Tippett has seen enough of his team coming up just short. The Coyotes (18-16-4) are 2-4-1 while playing seven consecutive one-goal games, the latest a 3-2 loss to Colorado on Thursday.
"It's frustrating. We've played a lot of tight hockey games and we can't find a way to get on top of them," Tippett said.
Phoenix's last five-game skid was Feb. 23-March 3.
"We're just not doing enough little things right right now and are making mistakes that cost us," captain Shane Doan said.
The Coyotes have killed all 18 penalties over the last six games, but they are 0 for 11 with the man advantage in their last four contests. Martin Hanzal -- tied for third on the team with six power-play points -- has missed the last three games with an lower-body injury.
Phoenix will likely be without starting goaltender Mike Smith on Saturday after the team placed him on injured reserve earlier this week with a groin injury.
Backup Jason LaBarbera should be in net for a fifth straight contest. He made 23 saves in the Coyotes' last game in St. Paul, a 6-5 overtime loss Jan. 2 that snapped Phoenix's three-game road winning streak in this series.
Koivu, who recorded a career high-tying four assists in that matchup, has two goals and eight assists during a five-game home point streak against the Coyotes.
Heatley scored Dec. 10 to register a point in his ninth straight game versus Phoenix. He has four goals and seven assists during that stretch.
Minnesota has won three of four over Phoenix following a five-game skid in the series.
AccuScore has powered more than 10,000 simulations for every NHL game on ESPN.com, calculating how each team's performance changes in response to game conditions and opponent's abilities. Each game is simulated and the game is replayed a minimum of 10,000 times to generate forecasted winning percentages.