Seguin, the No. 2 overall pick in the 2010 NHL entry draft, was traded to the Stars by Boston in July. He came into Friday night's game with only one assist this season in the two games Dallas had played.
Benn had two assists and Chiasson had one.
Blake Wheeler, with his first goal of the season, scored for the Jets.
In the first period, Winnipeg won the faceoff contest 15-9, a weak spot in their game recently, but were outshot 15-11.
But they lost the last minute of the power-play opportunity when Byfuglien's partner Toby Enstrom was sent off for hooking.
The Stars made good on their minute with an extra man when Seguin set up Chiasson, who stuffed one under Pavelec's pads at 9:33. Seguin then slapped in a drop pass from Rich Peverly to make it 2-0 at 12:09.
Benn finished the scoring in the first by tucking Brendon Dillon's rebound behind Pavelec's back at 16:35. Seguin was the second assist on that goal.
Seguin opened the scoring in the second to make it 4-0 when he slapped one into the net from the right faceoff circle, after both Winnipeg and Dallas had failed to connect on power-play chances.
Wheeler beat Ellis at the 5:35 mark of the third when he slipped in a rebound from Byfuglien's slapshot on a power play.
Winnipeg put on more pressure in the third, outshooting Dallas 44-31 by the end of the game, but it couldn't find the net. This was the first game the Jets have outshot an opponent this season.
With a power play late in the third, Winnipeg pulled Pavelec. But the Jets failed to score with two extra attackers.
Notes: Friday night's game was the fifth in a row where the Jets have scored a power-play goal, including a five-on-three Thursday night in St. Paul. They failed to score on a five-on-three last season and had the worst power-play percentage in the NHL.