Duchene gave the Stars a 3-2 lead at 6:55, taking a return pass from Tyler Seguin on a rush and roofing a shot over Andrei Vasilevskiy from below the right circle.
Hintz then extended the lead to 4-2 with a power-play goal at 7:53. He skated through the neutral zone with speed, got around Lightning defenseman Erik Cernak, and shot blocker side on a breakaway.
Miro Heiskanen and Evgenii Dadonov also scored for the Stars (13-6-0), who have won five of six. Jake Oettinger made 27 saves.
Anthony Cirelli scored twice for the Lightning (10-7-2), who were coming off a 7-6 overtime loss at the Columbus Blue Jackets on Thursday. Vasilevskiy made 24 saves.
Cirelli gave the Lightning a 1-0 lead at 4:09 of the first period, burying the rebound of Brandon Hagel's sharp-angled shot in the low slot.
Dadonov tied it 1-1 at 6:05 when Ilya Lyubushkin's one-timer from the point deflected in off his skate near the left post.
Cirelli put the Lightning back in front 2-1 at 8:34. He got the rebound of his own redirection in the low slot, spun and tucked a shot past the right pad of Oettinger.
Heiskanen tied it 2-2 at 15:49 of the first, taking a cross-ice pass from Duchene and scoring on a wrist shot from the left circle that beat Vasilevskiy glove side.
