PITTSBURGH — So here were the Rangers, facing overtime once again, facing overtime again just shy of 10 months after three of the most excruciating overtime losses possible, and after the last one left the taste of ashes in their mouths.

But not on their psyche, not for a moment.

“Never crossed my mind,” Ryan McDonagh said after Kevin Hayes’ goalmouth score at 3:14 of OT gave the Blueshirts a 2-1 victory Wednesday for a 3-1 lead over the Penguins with a potential clinching Game 5 coming up Friday at the Garden. “This is about this year.”

It of course would be foolish to suggest Hayes’ presence a year ago would have turned around the final. But it would be equally foolish not to recognize the impact the rookie free-agent signee out of Boston College has had on the 2014-15 Rangers.

Who says so?

Glen Sather, that’s who.

“Oh, it would be completely different,” the Rangers’ general manager told The Post as he strode toward the winners’ room. “Not only wouldn’t we have had him, but we would have had to go out and gotten somebody else [to fill the role as third-line center].”

Hayes, of course, had been the Blackhawks’ first-round selection at 24th overall in the 2010 Entry Draft, but eschewed the chance to sign with that western power in order to become a free agent after completing his senior year at Chestnut Hill.

The Rangers were giddy when they signed him, envisioning big things down the road from the rangy, 6-foot-5 center who will turn 23 next month. But they didn’t have to wait that long, as down the road turned into the present … a present that keeps on giving.

“No, I didn’t envision it would happen this quickly,” Sather said. “It’s very rare to be able to do what he’s done. He’s a very smart player, he learns quickly and he’s a great kid.

“The mistake I made was not getting his brother from Chicago,” he said, alluding to 25-year-old Jimmy Hayes, who bounced around the Blackhawks’ organization for a few years before landing in Florida last season. “I wanted to, but it just didn’t work out.”

But this otherwise was a no-regrets night for the Rangers, who were dreadful in a first period in which they mustered two shots on net, one at even-strength from long range, and fell behind quickly 1-0.

“It was as ugly as it gets. We were awful,” said McDonagh, who was a force over the final 43-plus. “Our legs weren’t moving, we weren’t playing anywhere close to the way we needed.

“We talked in here about the need to reset,” the captain said. “We challenged ourselves to at least give ourselves a chance to win.”

The Hayes-Marty St. Louis-Carl Hagelin unit had struggled big time in Games 2 and 3 after a decent opener. The line was nowhere through the first period. But the trio picked it up in concert with the rest of the team, drawing even at 17:15 of the second on Derick Brassard’s gritty goal from in front after strong plays by McDonagh and Rick Nash.

The line produced a passel of scoring chances in the second and maintained its posture through the third. And then, it was Hayes who struck after St. Louis made a strong play from behind the net to put the puck in front, off a skate, where Hayes’ long reach and cool took it over the finish line.

“The first three games, myself and our line were just average,” Hayes said. “We weren’t generating too much offense. We were holding our sticks too tight. But we got going in this one, creating offense, getting chances.”

The victory was the Blueshirts’ third by 2-1 in this series and fifth in six playoff games against the Penguins at their home rink over the last two playoffs. Of course, this series is not over, history tells us as much, but what was so impressive about this one was the way the Blueshirts stuck with it after stinking up the joint through the first 20 minutes. They refused to waver even if they wobbled.

Hayes doesn’t waver, either. Nothing seems to faze the young man, who never lets anyone see him sweat.

“That’s one of his strengths, that he is so laid back, on and off the ice,” said Big Time Brassard. “It helps with his confidence and allows him to be patient.

“I think this is going to be really big for him. He might not show it, but the playoffs are new for him. Last year, he was playing college hockey.”

Last year, the Rangers were losing three overtime games in Los Angeles. After last year, Henrik Lundqvist’s career overtime record was 6-15. This isn’t last year.

Hayes is a native of Dorchester, Mass. Growing up, many were the times he envisioned something like this.

“Every kid wants to do that,” he said through a smile. “I’m excited.”

Three down. One to go.

Three down. Thirteen to go.