The Lightning scored three goals on seven shots in the second period.
Hagel made it 2-1 on a snap shot from the left face-off circle at 8:52, and Alex Killorn pushed it to 3-1 on a wrist shot from the top of the left circle at 13:55 when he beat Vanecek to the short side.
"Obviously I'm playing with some Hall of Fame players with [Point and Kucherov]; everyone knows those names," Hagel said. "When you get those guys the puck, good things are going to happen, so a lot of credit to those guys. I just try and go out there and be the hardest-working guy on the ice."
Kucherov extended the lead to 4-1 on a backhand at the right post with 0.8 seconds remaining in the second.
"I looked up and I think [Kucherov] had the puck on the blue line with five seconds left and Point is a big part of that too," Cooper said. "Kucherov can finish in those areas, but probably the one that popped the balloon was definitely that fourth one."
NOTES: Cooper said Stamkos is day to day. ... Kucherov has a point in 11 of the past 14 games against the Devils (eight goals, 14 assists). ... Devils forward Miles Wood sustained an undisclosed injury late in the second period and did not return. Ruff had no update after the game. ... Forward Ondrej Palat had one shot in 16:02 of ice time against his former team for the first time since he signed a five-year contract with the Devils on July 14. ... Cirelli is the second player in Lightning history with a short-handed goal in consecutive games (Stamkos, April 4-6, 2019). … Forward Curtis Lazar had three hits in 10:07 of ice time in his Devils debut after being acquired in a trade with the Vancouver Canucks on March 3. … Hughes (37 goals, 43 assists) is the fifth United States-born player to reach 80 points in a season at age 21 or younger, joining Jimmy Carson (107 in 1987-88; 100 in 1988-89), Bobby Carpenter (95 in 1984-85), Jeremy Roenick (94 in 1990-91) and Patrick Kane (88 in 2009-10).