It was Vasilevskiy’s first shutout of the season and his 41st in the NHL.
Anthony Cirelli had a goal and an assist, and Nikita Kucherov had three assists for the Lightning (13-7-2), who have won four straight.
Samuel Ersson made 15 saves for the Flyers (11-7-3), who were beginning a four-game road trip.
Hagel gave the Lightning a 1-0 lead at 15:34 of the first period. He redirected a shot from Emil Lilleberg while battling for position in front with Emil Andrae.
Cirelli extended the lead to 2-0 at 16:00 of the second period, tapping in a centering pass from Hagel with his backhand on a 3-on-2 rush.
Hagel added an empty-net goal at 19:45 of the third period for the 3-0 final. He has seven points (four goals, three assists) in his past two games.
Tampa Bay played without forward Brayden Point and defenseman Erik Cernak. Before the game, coach Jon Cooper said Point, who left during a 5-3 win against the Washington Capitals on Saturday, is “dicey” to play against the Calgary Flames on Wednesday. Cernak is going to miss “significant” time.