Charle Eduoard D'Astous and Conor Geekie scored for the Lightning (1-1-0), who lost 5-1 to the New York Rangers in their season opener on Thursday. Brandon Hagel had two assists and Andrei Vasilevskiy made 19 saves.
Justin Sourdif scored for Washington (1-1-0), which beat the Carolina Hurricanes 5-2 in its season opener on Friday. Charlie Lindgren made 27 saves.
D'Astous gave Tampa Bay a 1-0 lead at 2:26 of the first period after Hagel sent a pass to him at the top of the right circle and he sent a wrist shot past Lindgren short side over the blocker.
Geekie extended the Lightning lead to 2-0 at 16:30 with a one-timer from the right circle that beat Lindgren to the stick side off a pass from Hagel.
Sourdif made it 2-1 at 7:04 of the second period after Jakob Chychrun sent the puck toward the net from the point and Sourdif redirected the puck past Vasilevskiy from the slot.
Guentzel added an empty-net goal at 17:55 off a pass from Nikita Kucherov for the 3-1 final. John Carlson, playing in his first game against his former team, also had an assist on the goal.