It was Oettinger's third shutout of the season and his 15th in the NHL.
Arttu Hyry and Adam Erne each had a goal and an assist for the Stars (45-19-12), who are 2-4-2 in their past eight games.
Connor Hellebuyck made 18 saves for the Jets (32-31-12), who had won four of five and are 6-3-2 in their past 11.
Duchene opened the scoring with a power-play goal at 9:43 of the first period. After his initial shot was stopped by Hellebuyck, the rebound bounced off the end boards back to Duchene, who then put the puck in off Hellebuyck's right hip from below the goal line to the left of the net.
The goal ended a streak of six games in which the Stars had allowed the first goal of the game.
Hyry made it 2-0 just 1:29 later at 11:12 when he beat a sprawling Hellebuyck with a snap shot from the bottom of the right face-off circle off a cross-slot pass from Jamie Benn. It was Hyry's second goal in the past three games after he scored his first NHL goal on Sunday.
Erne extended the lead to 3-0 at 2:15 of the second period. Lian Bischel sent a slap shot from the point that was tipped by Erne in the left circle low to the glove side.
