Andrei Vasilevskiy stopped shots by Ottawa’s Tom Pyatt and Matt Duchene in the shootout.
Tampa Bay threatened to win on a power play at the end of overtime, but Nikita Kucherov’s shot past Craig Anderson was launched a split-second after the buzzer.
Ottawa broke out on top in unusual fashion. Bobby Ryan was credited with an unassisted goal 6:31 into the game after Dan Girardi’s attempt to clear a rebound glanced off the shin of fellow Lightning defenceman Braydon Coburn and past Vasilevskiy.
Twelve minutes into the second period, Tampa Bay pulled even on a delayed penalty with a deflected goal of its own. Kucherov blasted a shot from the top of the right circle that glanced off teammates Tyler Johnson and Alex Killorn and through the legs of Anderson.
The Senators regained the lead on a backhander by Cody Ceci with 5:26 remaining in the second. Yanni Gourde tied it again just over a minute later.
Ottawa took its third lead six minutes into the third period on a power-play goal by Derick Brassard. Vladislav Namestnikov answered for Tampa Bay about five minutes later.
“Once we get the lead, we get a little passive, and that’s something that we’re going to have to work on,” Senators captain Erik Karlsson said. “We gave them a little too much room. We were up by a goal and we let them come back a little too easy. That’s going to happen, unfortunately, against good teams like this.”
Vasilevskiy needed to make only 18 saves in his league-leading 22nd victory. Anderson made 35 stops for Ottawa, which has lost all but three of its last 17 games.
“The second period we really tilted the ice,” Lightning coach Jon Cooper said. “Give Anderson credit. He was kicking everything out.”