CHICAGO — The feel-good energy the Rangers generated in the last two games largely evaporated in the span of a single period.

Facing a bottom-dwelling Blackhawks team, the Blueshirts blew a two-goal lead in the final frame before Mika Zibanejad salvaged the team’s good name by scoring the game-winning goal 2:37 into overtime to take a 4-3 victory that didn’t feel much like a victory Friday night at United Center.

“Obviously, you want the performance to be good,” said Zibanejad, who ended a seven-game goal drought with his second overtime score of the season. “We know we have to play better. The longer we go through the season, we want to build and we want to feel good about our game. Right now, it’s two points. Relieved that we got the win and we’ll move on.”

Head coach Peter Laviolette said the Rangers were consistently not where they needed to be throughout the night.

Even so, the Rangers had built a 3-1 lead on goals from Alexis Lafreniere, Chris Kreider and Jonny Brodzinski by the 9:02 mark of the second period after Blackhawks forward Alex Vlasic opened the scoring when goalie Igor Shesterkin was screened less than three minutes into the game.

The Blackhawks never stopped working.

The Rangers did, and it allowed the home team to score two goals in the span of 5:21 in the third period to turn the game upside down and earn their first point since Jan. 19.

This was a high-pressure game for Shesterkin, who made his first start since wrapping up a tough January. The Russian netminder ultimately gave up three goals on 31 shots in his first win since Jan. 21.

“I think we just got ahead and just thought the game was going to be easy,” said Brodzinski, who scored his fourth goal of the season and tied the career high he set with the Kings in 2017-18.

Chicago, without prized top-overall pick Connor Bedard (broken jaw) for the 13th straight game, had lost five in a row and nine of their last 12 entering Friday night’s contest.

Over that span, the Blackhawks had been shut out three times as they continue to sink further into last place in the NHL.

Everyone likes to say there are no easy games in this league, but the Rangers failed to put away a team that they have more than double the points on.

The Rangers had three power-play opportunities to do so and didn’t convert on any.

Coming into the game on an 0-for-11 skid with a mere 11 shots in the last five games, the top man-advantage unit continued to flail.

So much so that Laviolette sent the second unit out to start the Rangers’ third power play, an ultra-rare occurrence that underscores how little the star-studded first group has been generating.

“It’s a lot of overthinking,” Zibanejad said of the power play. “We’re talking about playing fast, but I think it’s just trying to find something, try to overdo it, try to overcompensate for what’s going on right now. We talk about simplifying and that’s what he need to keep harping on and keep getting better at. Obviously, we want the power play to get going again.”