Stone has five goals and three assists in his past four games. He went eight straight without a point prior to this stretch.
The Senators gave the Lightning their second loss in 12 games.
Zack Smith, Shane Prince and Jean-Gabriel Pageau also scored for Ottawa, and Craig Anderson made 31 saves. Pageau added two assists.
Andrei Vasilevskiy stopped 24 of 28 shots for Tampa Bay. J.T. Brown scored the Lightning's only goal.
For the second straight game, the Senators scored first and didn't let up, giving the 17,078 on hand at Canadian Tire Centre something to cheer about.
Smith got his second goal in two games by opening the scoring at the five-minute mark. Stone dropped a pass back to him, and he beat Vasilevskiy top corner.
Prince made it 2-0 late in the period with his first since Nov. 25, but the Lightning cut the lead in half 34 seconds later when Brown took advantage of a rebound and beat Anderson from in close.
Ottawa padded the lead early in the second on Stone's power-play goal, and midway through the period, Stone made it 4-1 after beating Vasilevskiy shortside.
Tampa Bay's best chance to respond came late in the second when Nikita Kucherov broke in, but Anderson easily made the save.
Lightning coach Jon Cooper pulled Vasilevskiy at 11:24 of the third in favor of the extra attacker, but the move backfired when Pageau scored on the empty net.
NOTES: Ottawa D Jared Cowen and LW Nick Paul, as well as Tampa C Jonathan Marchessault and D Matthew Carle were healthy scratches. ... The Lightning face Montreal on Tuesday night, while the Senators are back in action Wednesday night against the Detroit Red Wings.