CALGARY — Somehow the Rangers left Western Canada with a point after three tries, thanks to a 5-4 overtime loss to the Flames on Saturday night.

Trailing 4-1 with 4:57 gone in the third period, the Rangers turned into a nasty, desperate club, driving to the net at every opportunity.

Tanner Glass scored 16 seconds later, poking a loose puck in the crease past Jonas Hiller. Dan Boyle put a backhander past Hiller with 4:54 left in regulation. Derick Brassard’s long shot with goalie Antti Raanta pulled for a six-on-four attack tied the score at 4-4 with 1:12 remaining.

But with 2:51 left in overtime, TJ Brodie scored on a wrister to Raanta’s stick side to give the Flames the victory.

The Rangers trailed 5-3 in the third period Friday night in Edmonton, came back to tie and then lost. Asked why for the second straight game the team found a higher level of desperation and intensity only when trailing in the third period, Ryan McDonagh said: “You’ve got a good point. We’ve got to find that mentality right from the start of games and carry it through — the high-intensity level, guys hungry around the net — and continue to try to find goals.”

Said Marc Staal, “It’s like we’re too tentative to start, and causing us to second-guess our coverage, and then when we fall behind, we start playing like we need to score and stop thinking about it and we make plays to get us back in the game. We need to find that looseness like we’re behind, with the conscious effort of defending well. We can do it, but we’re not defending well enough to be able to take those chances to win games early on.”

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Before heading west, McDonagh said, “we thought our game was heading in the right direction. We certainly didn’t foresee this, coming out with just one point. I’m proud of the team, especially after what happened in Edmonton. We could’ve just folded and said, let’s go home. We’re very competitive in here, regardless of how it may look at times. ’’

The Blueshirts, who had forged a nine-game winning streak earlier this season, hadn’t lost three in a row during the same road trip since Oct. 8-12, 2013, in San Jose, Anaheim and San Jose in coach Alain Vigneault’s first season behind their bench.

But it happened again in Western Canada, sending the Rangers home limping under the weight of a 2-6-2 skid. The Blueshirts, the NHL’s best team on the road last season, are 6-5-3 away from New York.

The tide first turned late in the second period at the Saddledome. The Rangers held a 1-0 lead for the first 37-plus minutes until the Flames delivered a crushing blow, scoring twice in 17 seconds to go ahead 2-1. They extended the lead when Johnny Gaudreau raced up the middle untouched and beat Raanta for a two-goal bulge at 2:32 of the third period. Joe Colborne made it 4-1 at 4:57.

The Rangers went ahead 1-0 at 10:56 of the first period. McDonagh slid the puck to Dylan McIlrath, whose pass off the boards to Viktor Stalberg set up a give-and-go with Kevin Hayes. The puck went back to Stalberg in the right circle and he backhanded a pass to J.T. Miller driving the net. His deflection past Hiller was Miller’s fifth goal, on only the third shot of the period.

Stalberg was in the lineup for Jarret Stoll, who was a healthy scratch for only the second time this season.

The Rangers had been on their heels for the first seven minutes, with Raanta, who had relieved Henrik Lundqvist early in the third period in Edmonton on Friday night, forced to make seven stops, including during an interference penalty on Mats Zuccarello at 3:54. Raanta had made 22 saves in a 4-1 defeat of the Flames at Madison Square Garden on Oct. 25.

Miller’s goal seemed to relax the Blueshirts a bit, and play evened out for the rest of the period, with the Rangers more cohesive and providing more puck support than in the 7-5 loss in Edmonton.

But the Flames struck twice in the final minutes of the second period. Keith Yandle’s misguided clearing pass was easily picked off by Gaudreau, who zipped a shot past Raanta’s glove with 2:19 left. After a gaffe by Dan Girardi, Mason Raymond finished off a two-on-one with Michael Frolik to put the Flames ahead with 2:02 remaining.