The shutout was Vasilevskiy’s second of the season and 36th in the NHL.
Vasilevskiy was honored for earning his 300th win on Thursday during a pre-game ceremony that featured congratulations from Hall of Fame goalie Martin Brodeur and former Lightning goalies Nikolai Khabibulin and Ben Bishop.
Victor Hedman and Anthony Cirelli each had a goal and an assist, and Nick Paul also scored for the Lightning (9-6-1), who have won two in a row following a four-game skid. Nikita Kucherov had two assists to extend his point streak to seven games (three goals, nine assists).
Jacob Markstrom made 22 saves for the Devils (12-7-2), who had won five of six (5-1-0).
Paul gave Tampa Bay a 1-0 lead at 14:27 of the first period when he scored on a shot above the right circle with Gage Goncalves providing a screen in front of the net.
Darren Raddysh scored his first goal of the season 39 seconds into the third period to make it 2-0, a one-timer from the right circle after Cirelli won a draw in the zone and Nikita Kucherov provided the set-up pass.
Hedman scored on the power play to extend it to 3-0 at 7:40, a slap shot from the point.
Cirelli scored an empty-net goal at 19:48 for the 4-0 final.
