Jamie Benn struck twice for the Stars (22-19-7), while Colton Sceviour, Ales Hemsky and Trevor Daley had goals as well. Kari Lehtonen made 25 saves.
Mika Zibanejad, Bobby Ryan and Alex Chiasson scored for the Senators (19-19-9). Robin Lehner, making his first start since January 13th, stopped 33 shots.
Thursday's game marked Jason Spezza's return to Ottawa for the first time since being traded to the Stars in the off-season. While few knew how the former Senators captain would be received, the 18,752 on hand gave Spezza a standing ovation following a video tribute early in the first period.
The Stars took the 4-3 lead midway through the third period, as Klingberg took advantage of an Ottawa turnover to break in alone and beat Lehner with a wrist shot.
With just under a minute remaining in regulation, and Lehner on the bench, the Senators caught a huge break when Tyler Seguin took a hooking penalty, but a lost faceoff resulted in Daley wristing a puck all the way down into the empty net to seal the victory. Benn added a second empty-net goal to round out the scoring.