The Rangers were on their last legs, but they willed themselves to the finish line in a game that they had no business being in, let alone winning.

In their 2020-21 season finale, Mika Zibanejad scored two of the Blueshirts’ four third-period goals in a 5-4 victory over the playoff-bound Bruins on Saturday at TD Garden. The last five losses certainly didn’t make for the high note on which the Rangers hoped to go out, but they made the last one count.

“It means more than what you would think right now,” Zibanejad said after the win.

This wasn’t expected, given the fact the Rangers took the ice with a depleted lineup that featured four players who spent most of the season in the AHL. Not to mention the mental and physical toll this past week probably took on the Rangers, from the beating they endured against the Capitals to dealing with the aftermath of a shocking front-office change.

“These last 10 days, it just felt so bad,” head coach David Quinn said. “Just the way things have gone and all that’s going on within our organization. You kind of forget that you want to judge your season by the totality of it. To be in a hunt, up to 10 days ago, it seems like 10 years ago, and not have [Jacob] Trouba and [Chris] Kreider for those two games against the Islanders [losses on April 29 and May 1], that is so pivotal for us.

“To lose those two guys, losing the way we have lately, and obviously with what’s going on within the organization with the [Tom] Wilson incident and Jeff [Gorton] and [John Davidson] situations, it’s been difficult. It was great to finish the way we did.”

With the score tied 1-1 heading into the third period, the Bruins’ perfection line capitalized on a turnover by Pavel Buchnevich 21 seconds in with a goal from David Pastrnak. But while Boston seemingly expected the Rangers to lay down after the exhausting week they had, the Blueshirts did the opposite.

The Rangers potted three straight goals in the span of 4:14 early in the third period to take a 4-2 lead.

After a spurt of stellar passing failed, the Rangers tried it again, and this time Zibanejad finished the play. Alexis Lafreniere scored two minutes later, and then so did Vitali Kravtsov, giving the Rangers a two-goal lead.

The Bruins’ Brad Marchand and Patrice Bergeron forced the Rangers to dig deep, recording a goal each in the final six minutes in an attempt to avoid what they surely knew would be an embarrassing loss. But Zibanejad’s second goal of the game, sandwiched between those Boston scores at 18:07, proved to be the game winner.

Playing without Kaapo Kakko (who was out for precautionary reasons), Artemi Panarin, Jacob Trouba, Chris Kreider and Ryan Lindgren, the Rangers rallied to avoid finishing their season on a losing streak and to beat a Bruins team with legitimate Stanley Cup aspirations.

And goaltender Keith Kinkaid, making his first start since March 28 and just his seventh of the season, played a major role in the win. He recorded 28 saves on 30 shots before heading to the locker room with 11:10 left in regulation due to an injury. Igor Shesterkin finished the job with seven saves on nine shots.

So it all came to an end, with the Rangers finishing the season at 27-23-6. The team was dilapidated in the final few games, but they went out with their heads held high.

“You want to go out on a winning note because you’re going to carry whatever happens today throughout the summer,” Quinn said. “We talked about it from an individual standpoint and, collectively, a team standpoint. I thought our guys did a hell of a job, we showed a lot of characteristics you’re going to need moving forward.”