Of the seven pucks that wound up in the back of the net Monday night, five were directed over the goal line by the Wild.

But only three of them actually counted for the team.

The Devils were the beneficiaries of two fluky goals — on a measly six shots — to get a much-needed head start that helped buoy them until they found their rhythm to pull out a 4-3 overtime win over the Wild in front of 19,048 at Xcel Energy Center.

"Playing catch-up is difficult," coach Bruce Boudreau said. "It's wearing on you. It's tiring on you. So I think we're a pretty good team with the lead, but we gotta be able to get the lead and keep the lead."

The result wasn't exactly indicative of the action on the ice, as the Wild outshot the Devils 36-25, including 12-3 in the first period, but the team struggled to translate that pressure into production until the third when winger Mikael Granlund scored twice to erase a two-goal deficit.

That momentum, however, didn't carry over to the extra period.

Just 52 seconds in, defenseman John Moore one-timed an Adam Henrique feed past goalie Devan Dubnyk for the clincher — this after the Devils didn't register a shot on Dubnyk until 9:01 had been played in the first.

But New Jersey still managed to smuggle a lead into the intermission.

Winger Brian Gibbons' centering shot deflected off Henrique and loitered in the crease before getting nudged in by defenseman Gustav Olofsson's glove at 18:32 while Olofsson was tied up in the blue paint with Dubnyk.

"I was kind of waiting for Duby to maybe grab it or the whistle to blow, and it just didn't," Olofsson said. "Kind of went off my hand, so it was frustrating."

The Wild went on the power play just 14 seconds into the second, and that was just the boost the team needed to finally solve goalie Cory Schneider, who made 12 first-period saves and 33 in total.

Video (00:28) Wild coach Bruce Boudreau discussed the 4-3 overtime loss to the Devils on Monday.

After accepting a feed from Granlund at the top of the crease with his back to the net, winger Nino Niederreiter turned and shot on Schneider and the puck eventually trickled in at 1:32 to tie it at 1.

It was the fourth consecutive game in which Niederreiter has scored, a career-best run, and the goal extended Niederreiter's point streak to a career-high six games.

Meanwhile, Dubnyk remained relatively idle at the other end with the Devils boasting only five shots through the early stages of the second until No. 6 also found a fortuitous path over the goal line.

At 7:24, defenseman Steven Santini's shot from along the wall caromed off Olofsson and by Dubnyk to put the Devils ahead 2-1.

"It was frustrating," Olofsson said. "You can try to blame it on puck luck or whatever, bad bounces, but I think I gotta be better from the start."

The Devils looked rejuvenated after that and at 7:19 of the period, they finally scored a goal that didn't bank off a Wild player when defenseman Will Butcher jumped into the rush and wired a shot over Dubnyk's glove.

Still, the Wild persisted.

Granlund's shot through traffic went five-hole on Schneider on the power play at 11:14 to halt a six-game goal drought. The Wild's power play went 2-for-4, while the Devils blanked on two chances.

Later, with Dubnyk on the bench for the extra attacker, Granlund scored off a slapshot with 1:36 to go — execution that the team could have used earlier in the game.

"We had the puck for long periods of time tonight," said Dubnyk, who had 21 saves. "We just have to find ways to penetrate and get greasy ones when the other team is going to play that way."