Some wins just taste sweeter than others, and the Rangers should savor this one against the Metropolitan Division-leading Hurricanes.

After trailing for a majority of the game’s first 40 minutes, the Blueshirts made their first and only lead count. K’Andre Miller scored the game-winning goal just over halfway through the third period, when the 22-year-old defenseman tipped in a Mika Zibanejad shot from the top of the zone to help propel the Rangers to a 5-3 win over the Canes on Tuesday night at Madison Square Garden.

The Hurricanes appeared well on their way to their 12th straight win, which also would’ve extended their point streak to 18 games in a row, but the Rangers buckled down just in time to deny their division foe the satisfaction.

“Obviously, they’ve been one of the hottest teams in the NHL the last number of games and a top team in the league,” head coach Gerard Gallant said. “We weren’t perfect tonight, we got some puck luck, we were fortunate in that. It’s a big win, it’s a good game for us and we’ve got to continue to build off games like this.”

Every time the Rangers pulled even and tried to catch their breath, the puck would drop at center ice and the Hurricanes were already swarming the offensive zone to retake the lead. Twice, the Rangers’ goal announcement hadn’t even been made before Carolina scored another to keep the home team at a one-goal distance.

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Jacob Trouba’s power-play goal may have made it a 1-1 game in the first period, but that score only lasted 16 seconds.

The Rangers got caught puck-watching at the other end as the Hurricanes’ Andrei Svechnikov fed Martin Necas for a one-timer that gave Carolina the lead going into the first intermission.

Zibanejad’s pass attempt to Vincent Trocheck on the power play may have slid right through Canes goalie Pyotr Kochetkov to knot the game at two-all in the second period, but that score only lasted 29 seconds.

The Rangers couldn’t break the puck out of their zone, which allowed Hurricanes’ defenseman Jalen Chatfield to score off a tip by Filip Chytil for the 3-2 lead going into the second intermission.

It wasn’t until Artemi Panarin’s game-tying tally 36 seconds into the third period that the Rangers actively braced themselves for the Hurricanes’ retaliatory push. Third time’s the charm. Still, the Rangers scored just in time to give themselves a chance against the No. 2 team in the NHL.

“Third time, that’s enough for us to understand,” said Panarin, who now has points in 11 of his last 15 games.

The Rangers’ edge in the special teams battle allowed them to remain within striking distance of the Hurricanes. Going 3-for-5 with the man-advantage, including Chytil’s empty-netter in the third period, the Rangers kept themselves in the game as they worked to grind through Carolina’s relentless forecheck.

“They’re a hard team to play against,” said Vincent Trocheck, who ;eft the Hurricanes signed with the Rangers as a free agent last offseason. “They play the same way every night. They’re tight too, work hard on the forecheck. It’s just a matter of breaking that forecheck. You’re not going to prevent them from doing what they do. It’s just a matter of going out there and executing our system the way we can.”