Following numerous chances from the Stars, Hintz collected the rebound from a Jason Robertson shot in front and lifted it over a sprawling Linus Ullmark.
Robertson had a goal and two assists, Mikko Rantanen had a goal and an assist, and Jake Oettinger made 27 saves for the Stars (10-4-3), who won their third in a row and first in nine attempts in Ottawa.
Drake Batherson and Nick Jensen each scored for the Senators (8-5-4), who extended their point streak to six games (3-0-3). Ullmark made 30 saves, including 16 in the third period.
Batherson gave the Senators a 1-0 lead just 49 seconds into the game when he took a cross-ice pass from Jake Sanderson and beat Oettinger over the right shoulder with a wrist shot from the left face-off circle.
Jensen pushed it to 2-0 at 8:53. Pinching from the blue line, Jensen finished a passing play with Michael Amadio and Claude Giroux by chipping the puck over Oettinger’s glove in tight.
Ottawa defenseman Thomas Chabot, who took a hard hit from Colin Blackwell midway through the first, did not return for the second period due to an upper-body injury.
Rantanen cut it to 2-1 at 16:22 of the second period. After forcing a turnover at the Stars’ blue line, Rantanen broke down the ice, accepted a stretch pass from Robertson and beat Ullmark five-hole with a snap shot on a breakaway.
Ullmark made back-to-back saves lying on his side to keep it 2-1 midway through the third period, the first with his glove on Alexander Petrovic and the second with a double-pad stack on Wyatt Johnston.
Robertson beat Ullmark over the glove with a wrist shot from the high slot on a power play to tie it 2-2 at 8:00.
