Zack Smith scored twice for the Senators (13-11-3) and Craig Anderson had 31 saves to hand the Lightning its fourth straight loss.
Tampa Bay is now 11-15 on the year, with a 4-11 record on the road.
Bruno Gervais and Martin St. Louis had the tallies for the Bolts and Dwayne Roloson made 27 saves in the loss. Steven Stamkos's two assists extending his points streak to seven games, currently the NHL's longest.
Monday night's game was the first of a four-game road trip for Tampa Bay and the Lightning have just three wins in its last 11 contests.
The Lightning had the right idea shooting the puck more, but still came up short.
Tampa Bay defensemen Bruno Gervais, who was in the lineup because Pavel Kubina was sidelined due to a lower body injury, scored the games first goal at 13:52 of the second period. Gervais's wrist-shot was his second goal of the season while Steven Stamkos and Marc Andre Bergeron added the assists. The goal came after Tampa had plenty of missed opportunities in the first period. Less than three minutes later, the Senators evened the game up at two after Smith tipped a goal in past Roloson.
The Lightning made it a 2-1 game at 3:55 of the third period after Stamkos took advantage of Karlsson's turnover at the blue line, which fed a wide open St. Louis to give Tampa its second lead of the game.
The Senators were able to tie the game with a timely play by their goaltender. Anderson played the puck to Jason Spezza. Spezza then dropped the pass to Alfredsson who beat Roloson with a shot from the top of the circle.
The goal was a bad one for Roloson to give up and he should have saved the shot from that angle.
That goal sparked two more for the Senators, who scored three goals in a seven minute span. Nick Foligno scored the game winner at 15:33 after getting Alfredsson's rebound. Smith then scored his second goal of the night 46 seconds later on a Sergei Gonchar pass. On both goals, the Lightning defensemen showcased a slower than desired effort getting back in the zone.