The Stars fired three second period goals in under five minutes to take control of the contest.
"We had lots of chances in the first period and we didn't score," said Faksa. "But our team showed lots of heart. We played the same game in the second period and we get rewarded and we score three goals in the second period.”
Esa Lindell also scored for Dallas, who kicked off a four-game road trip with a win to move to 39-31-6.
Alexander Radulov had a pair of assists for the Stars.
The Jets dropped to 45-27-4 but held onto first place in the NHL's Central division with a slim two point lead over Nashville, who beat the Minnesota Wild Monday night.
Kyle Connor and Patrik Laine scored for Winnipeg.
Connor Hellebuyck made 32 stops for the Jets, who are now 1-1 on their four game homestand, their final one of the season.
There was no scoring in the first period.
Esa Lindell got Dallas on the board 10:27 into the second period, snapping a wrister through a screened Connor Hellebuyck to make it 1-0.
The goal was his 10th of the season.
Radek Faksa made it 2-0 just under two minutes later when he was sent in alone by Blake Comeau and fired a wrister past Hellebuyck, beating him low glove side at 12:23.
The goal was his 14th of the season.
Tyler Seguin scored on a two-man advantage to make it 3-0 at 15:16 when Jamie Benn threaded the needle and hit him with a cross slot pass from the side of the net.
Seguin snapped a wrister past Hellebuyck from the left faceoff dot to score his 30th of the season.
Seguin scored at 10:34 of the third period after Miro Heiskanen skated into the slot before feeding Seguin at the side of the goal.
The Dallas forward kicked the puck from his skate to his stick before beating Hellebuyck just under the crossbar to make it 4-0.
Kyle Connor got the Jets on the board at 11:03, converting a nifty Kevin Hayes feed to make it 4-1.
The goal was his 33rd of the season.
With Radek Faksa off for high sticking, Patrik Laine fired a power play goal, one timing a Jacob Trouba from inside thean right faceoff circle feed past Bishop to make it 4-2 at 15:10.
The goal was his 30th of the season.
Laine joins Gretzky, Dale Hawerchuk and Jimmy Carson as the only NHL players to score 30 goals before the age of 21.
But he wasn't celebrating that factoid after the game.
“Well, right now nothing really," said Laine.
"It doesn’t make me happy right now after that kind of game. But obviously it’s a pretty good accomplishment for me, just a guy from Finland who was dreaming about being in the NHL and now scored 30 goals three times right away so I gotta be proud of myself but the work is just beginning."
Jets captain Blake Wheeler said Dallas played a tough defensive game.
“There is certainly a style of play that factors in. Nashville plays that style of game, Dallas is one of the better defending teams in the league. They suffocate the life out of you and they have a pretty good goalie back there, too. So when you get a chance, you have to take advantage of it. If you’re giving up four against that team, it’s going to be tough. That’s kind of where it stood tonight and we just didn’t quite do enough of what the game demanded to get the job done.”
Stars veteran Andrew Cogliano said they didn't see the Winnipeg Jets best game.
“I thought we played a really good game. All four lines were going early. We played a perfect road game. I thought we just deserved to win. We came in and we were determined to win tonight." "I don't think that was their (Jets) best game. I know they're a lot better team probably than what they showed tonight, but I think credit to us. I thought we played a good, hard game and were tough to play against," he said
Dallas Head Coach Jim Montgomery was pleased with the result but moreso with his team's performance on the road this season.
"You're happy to be able to beat the Winnipeg Jets. I mean it's an elite hockey team in this league and one of the top teams in the league. More importantly for us a goal for us this year was to be a better road team and to also be better within our division and we've accomplished that this year."
SHOTS-DALLAS 37 WINNIPEG 23