Hagel has eight goals in the past five games and 12 in November, tied with Dallas Stars forward Jason Robertson for the most goals this month.
Nikita Kucherov had three assists to run his point streak to nine games (four goals, 14 assists), including five straight multi-point games. Nick Paul and Jake Guentzel scored, and Jonas Johansson made 10 saves for the Lightning, who outshot the Rangers 35-11.
Tampa Bay (16-7-2) has won 15 of its past 18 games, including four in a row without forward Brayden Point, and defensemen Victor Hedman, Erik Cernak and Ryan McDonagh, each out with an injury.
Igor Shesterkin made 31 saves and J.T. Miller scored for the Rangers (13-12-2), who had a three-game winning streak end. Their 11 shots on goal were a season low.
Hagel gave the Lightning a 1-0 lead at 10:53 of the first period. His shot from the top of the left face-off circle went in off Rangers defenseman Carson Soucy’s right skate.
Hagel made it 2-0 at 8:57 of the second period. He took a stretch pass from Kucherov in for a breakaway on Shesterkin, who did the splits and stopped Hagel’s initial shot with his left pad. But Hagel recovered the puck in the slot and lifted it over Shesterkin’s pad.
Miller got the Rangers within 2-1 at 17:31 of the second. Adam Fox carried the puck through the right circle and moved it across the slot to Miller at the left post, where the puck went in off his right skate.
Paul made it 3-1 at 2:02 of the third period. Kucherov, who was below the goal line on the right side, found Paul in the slot for a redirect on his forehand.
Guentzel scored into the empty net at 19:42 for the 4-1 final.
Fox left the game because of an upper-body injury with 12:57 remaining in the third period after getting hit hard and sandwiched into the end boards by Hagel. He was holding his left arm as he left the ice.