First a shot by Wild center Joel Eriksson Ek rolled behind the Hurricanes’ James Reimer before the goaltender cleaned up the rebound.

Then the puck trolled the Wild again when winger Jordan Greenway’s heave skirted the goal line and grazed the post.

Either one would have broken a third-period tie, a nudge that would have completed yet another come-from-behind win.

Video (01:05) Coach Bruce Boudreau recaps the 4-3 overtime loss to the Hurricanes Saturday.

Instead, the Wild had to settle for just a point from a 4-3 overtime loss to Carolina on Saturday afternoon in front of 17,101 at Xcel Energy Center — an outcome that kept its point streak on home ice alive (4-0-2) and yet was still a frustrating finish.

“I still can’t believe it, to be honest with you,” Greenway said about his near goal. “What are you going to do? I don’t know if I could have shoved it any harder. We had great chances. Some of them found the net. Some of them didn’t.”

As has been the case with the Wild (7-11-2), the extra session also wasn’t much help.

After Greenway and Eriksson Ek’s linemate Luke Kunin was turned aside in tight, the Hurricanes stormed the other way and Andrei Svechnikov capitalized on a rising shot at 1 minute, 33 seconds.

“I would think that he would like to have that one back,” coach Bruce Boudreau said of goalie Devan Dubnyk.

The Wild is 12-30 in games resolved in overtime since the 3-on-3 format was implemented in 2015-16, this after Boudreau discussed deploying a new strategy following its previous and only other overtime setback to the Blues on Nov. 2.

“It’s really frustrating,” Boudreau said. “… It’s like penalty killing. Your goalie is your best penalty killer, right? It’s the same thing in all situations.”

Dubnyk, who’s 20-27 in his career in overtime, totaled 24 saves. Reimer made 32.

“It’s like nothing’s going on either way, and then all of a sudden it’s just like bang and it’s over,” Dubnyk said. “You don’t want to start letting that creep [in] where you’re worried or approaching things differently entering overtime because that’s the way it’s gone.”

It looked like the Wild might not need more time based on how it responded from getting down 2-0, the fifth time in the past six games that’s happened. Joel Edmundson’s point shot deflected off Kunin’s stick en route to the back of the net at 3:56 of the first and only 2:01 after that, Brock McGinn buried a rebound.

“We make it pretty tough on ourselves trying to overcome deficits every game,” winger Zach Parise said.

But that’s exactly what the Wild did.

Kunin’s shot flew in at 4:27 of the second and after Warren Foegele answered back with his own one-timer, Parise was all alone in front to convert on his backhand at 15:43. Just 1:21 later, defenseman Carson Soucy scored his first career NHL goal to tie it at 3.

“A lot of teams would have buckled, and it made our team stronger,” Boudreau said.

Parise’s goal, his second in as many games, was the Wild’s first shorthanded goal of the season. The Wild went 0-for-3 on the power play, while the Hurricanes were 0-for-2.

Eriksson Ek and Greenway had the best looks in the third, and Eriksson Ek ended up logging a career-high 20:04. The six shots on net by Eriksson Ek were also the most he’s had in a game in 2019-20 and overall, the three combined for 11 shots.

“That’s going to be a great line or a great threesome in the future for this team,” Boudreau said.

And in flashing that potential in the present, the unit nearly led the Wild to victory.

“You’d think at one point the puck luck would turn around a little bit,” Boudreau said. “But you’ve got to keep persevering.”