The Senators have lost five straight going 0-3-2.
Trailing 5-4, Ottawa had a great opportunity to tie the game as Callahan took a penalty with 55 seconds remaining in regulation. With Lehner on the bench, the Senators had a two-man advantage, but were unable to beat Bishop.
Callahan's power-play goal midway through the third had given the Lightning a 5-3 lead, but the Senators made it a one-goal game as Michalek deflected a Karlsson shot from inside the blue-line at 17:07.
Brewer scored his first goal in 95 games to give the Lightning a 4-3 lead at 3:48 of the third with a great shot off his backhand to sneak the puck in under the crossbar.
Hemsky made it 3-3 after displaying some great puck handling before beating Bishop late in the second. The goal earned him a standing ovation from the 17,136 on hand.
The Lightning had taken a 3-2 lead at the five-minute mark of the second on a power-play goal by Filpulla, who knocked home a rebound just out of Lehner's reach.
The Senators ended the first period tied 2-2 after getting off to a horrible start. Purcell, who hadn't scored in his last 19 games, opened the scoring just 23 seconds into the game.
Ottawa managed to tie the game on MacArthur's short-handed goal midway through the period. It was MacArthur's 21st of the season, tying a career high.
The Lightning regained the lead on Purcell's second of the night as he managed to dig the puck out through traffic in the crease and then shoot it in off the post.
Karlsson rounded out the scoring with a power-play goal, beating Bishop with a shot from just inside the blue-line.
Notes: G Craig Anderson (upper body injury) and G Nathan Lawson (lower body injury) missed the game. D Patrick Wiercioch and LW Matt Kassian were a healthy scratch for the Senators … The Lightning signed free agent forward Cody Kunyk to a one year, two-way NHL contract. Kunyk, 23, skated in 37 games for the University of Alaska-Fairbanks Nanooks this season, posting 22 goals and 43 points. D Keith Aulie, D Mark Barberio, C Tom Pyatt and RW Nikita Kucherov were healthy scratches for Tampa.