It was Lilleberg’s first three-point game in the NHL.
Brandon Hagel and Charle-Edouard D'Astous each had a goal and an assist for the Lightning (45-21-6), who extended their point streak to seven games (5-0-2). Andrei Vasilevskiy made 26 saves.
The Lightning were without forwards Nikita Kucherov and Nick Paul, who were both late scratches because of an illness. They are questionable for Sunday's game against the Nashville Predators.
Tampa Bay moved into first place in the Atlantic Division, with one game in hand over the Buffalo Sabres, who also have 96 points.
Dylan Cozens and Jordan Spence scored for the Senators (38-25-10), who had points in five straight (4-0-1). James Reimer made 23 saves.
Ottawa is one point behind the Columbus Blue Jackets for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Cozens gave the Senators a 1-0 lead 18 seconds into the game with a shot from the low slot that beat Vasilevskiy five-hole.
Spence extended it to 2-0 at 4:25 when he knocked in a rebound into the open net after Vasilevskiy went out of position to make a sprawling save on Nick Cousins.
Hagel made it 2-1 at 3:37 of the second period with a chip past Reimer from close range after D'Astous dug the puck out from traffic at the goal line.
D'Astous tied it 2-2 at 5:14 with a shot above the hash marks that beat Reimer stick side off a pass from Yanni Gourde.
Lilleberg put the Lightning ahead 3-2 at 8:51 of the third period when he finished off a 3-on-2 rush with the backhand.
Jake Guentzel made it 4-2 with a breakaway goal at 17:48 with Corey Perry providing the pass to start the play.
