There was no reason to think the Wild would struggle Wednesday night.

After all, it was riding a six-game winning streak into a game at Xcel Energy Center against Phoenix, which had lost six in a row.

But for 59 minutes, the Coyotes had the better of play in front of 19,076 fans who are battling playoff fever.

Then, in the final minute of regulation, Ryan Suter scored his first home goal in a Wild jersey to tie the score, and Mikko Koivu won it 2:43 into overtime as the Wild prevailed 4-3.

“We can play better,” a relieved Koivu said. “Phoenix made it hard for us. But you try to find a way to make a play when you can.”

Koivu came out of the right corner as a 4-on-3 power play was expiring and jammed a shot past Coyotes goalie Jason LaBarbera. Antoine Vermette put Phoenix in a precarious position when he cross-checked Wild defenseman Jared Spurgeon 35 seconds into the extra session, giving the Wild two minutes of sustained pressure in the Coyotes end.

“I don’t know if we would have handled this as well, trailing in the third period, at the beginning of the season,” Wild coach Mike Yeo said. “I just don’t think we played a good game, but we found a way to win.”

Suter’s tying goal came with 54 seconds remaining in the third period. With goalie Niklas Backstrom pulled, Suter’s shot from the left circle forced overtime.

“Sometimes, you just got to grind it out,” said the defenseman, signed on the Fourth of July. “We’ve had some nice games lately, but this one we had to grind it out.”

Backstrom had 24 saves, and LaBarbera stopped 33 shots.

“There was good and bad in the game,” Wild center Matt Cullen said. “We won, but we got a wake-up call. In a way, it’s good to come and grind one out. But we have to start better. We can’t let a team get back in the game.”

Defenseman Michael Stone gave Phoenix, which rallied from two goals down, a 3-2 lead two minutes into the third period.

Coyotes captain Shane Doan charged the net and had his right-side attempt stopped by Backstrom, but the rebound was cleared to the right point and Stone found Backstrom out of position with a well-aimed shot.

In addition to his rough finish, LaBarbera had a rough start. The Wild took a 2-0 lead early in the second period when he foolishly tried to clear the puck from behind his net through the right circle. Cullen had the good stick and picked the puck out of midair before hitting the yawning net.

But the Coyotes got second-period goals from Rob Klinkhammer and Boyd Gordon to tie the score before the period ended.

“You have to give Phoenix credit,” Koivu said. “They made it hard. They made us work.”

Torrey Mitchell of the Wild’s fourth line got the only goal of the first period, stuffing the rebound of a Mike Rupp shot through traffic.

Backstrom started his 12th consecutive game, a combination of necessity (with backup Josh Harding sidelined because of symptoms related to multiple sclerosis) and success (the Wild has the sixth-best goals-against average in the NHL at 2.35).

Backstrom might finally get a break when the Wild plays at Dallas on Friday night.

Darcy Kuemper, who is currently his backup, or Matt Hackett, who is playing for Houston of the American Hockey League, might get a start instead.