Hagelin's tally off a Taylor Pyatt assist with 5:13 remaining handed the Rangers a 3-1 lead and New York withstood a Lightning charge to notch their third win in four games.
Pyatt finished with two assists while Derek Stepan and Rick Nash also scored for the Rangers.
Steven Stamkos scored his sixth and seventh goals of the season for the Bolts, whose five-game winning streak was broken.
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