The Devils have made this first-round series against the Rangers competitive again.

Dougie Hamilton scored 11:36 into overtime to keep the Devils’ spirits alive and hand the Rangers a 2-1 loss Saturday night at Madison Square Garden, which prevented the home team from strengthening their already strong grip on this series.

“When we’ve been challenged and we’ve been down we have always answered the call this year — always,” Devils head coach Lindy Ruff said after his team’s win, which cut the Rangers’ series lead to 2-1.

The contest simply played more to the Devils’ style than the Rangers. With the score tied at one-all in the third period, the game turned into a track meet and the Devils were able to counter any offense the Rangers generated. That carried into overtime, as well.

And that was just what the Devils needed to alter the trajectory of the series.

Not only did the Devils’ adjustments on the penalty kill pay off, but also the Rangers fell back into their habit of making one too many passes (which had plagued them for parts of the regular season), allowing the visitors to keep the game close.

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The Rangers, who played straight-line hockey in Games 1 and 2, were suddenly looking for the perfect play and forcing it at times in pursuit of the best-looking shot again.

“We tried to get a little cute, I think,” head coach Gerard Gallant said. “I thought we played well. If those would’ve been put in the back of the net, I wouldn’t be saying what I’m saying now. They make their plays, we’ve got some talent, but sometimes a little more direct and making it hard on that younger goaltender. He made some key saves, both goaltenders were excellent tonight.”

It’s true, Rangers netminder Igor Shesterkin was just as sharp as he had been through Games 1 and 2. The Devils, however, made a bold switch in net by pivoting from the goalie who backstopped them for a majority of the season, Vitek Vanecek, to 22-year-old rookie Akira Schmid.

Schmid, who found out he was making his playoff debut after the Devils’ team dinner the night before, finished with 27 saves during regulation and was strong in overtime with eight stops.

The Devils have altered their lineup, in personnel and alignment, in every game so far in this series.

In addition to the change in goal, the Devils’ lines and defensive pairs underwent changes as well. To say that was a key in the victory might be a stretch, aside from the goalie switch. It may have been the Devils’ strongest performance of the series, but they still needed overtime to get the job done.

After scoring at least twice in each of the last two games, the Rangers’ power play was stifled in Game 3. They went 0-for-5 in the loss, which included whiffing on a late third-period man advantage. The Rangers’ power play has been key thus far, so their offense was clearly missing its contributions.

“Yeah, maybe. I think they came up with some big blocks, too,” Mika Zibanejad said. “When they get in front, maybe you don’t feel like you have the lane and you’re trying to look for someone else to get a better opportunity. I thought as the game went on, we put more pucks to the net and I think that’s what we’ve got to keep doing.”

Chris Kreider scored his fifth goal of the series to open the scoring at 3:39 of the second period, taking a forced turnover from Patrick Kane onto a two-on-one rush with Zibanejad before sniping it over Schmid’s shoulder.

With the goal, the longest-tenured current Ranger became the first player in franchise history to record five or more goals through the first three games of a single postseason.

This may have been the Devils’ best game and the Rangers’ worst of the series so far, but both clubs know it’s far from over.

Game 4 at the Garden is slated for Monday night, giving the Rangers a chance to redeem themselves in front of their home crowd.