Lehtonen made 31 saves to earn the win.
Hanzal tied it at 2 just 45 seconds into the middle period, one second after Jordie Benn's holding penalty expired. After Ekman-Larsson's slap shot from the right point bounced to Hanzal at the right side of the crease, Hanzal pulled the puck back from behind the goal line, and bounced it between Lehtonen's glove and the post.
Just 21 seconds after Dillon fought Kyle Chipchura, Ryder notched his fourth goal of the season with a wrist shot from the left circle that deflected off Ekman-Larsson's skate and inside the left post at 14:14.
Roussel, the eighth NHL player born in France, put Dallas ahead 1-0 at 9:53 of the first period. Roussel slipped behind Coyotes defenseman Michael Stone, sped in alone, and beat Smith with a nifty backhander over the glove.
"Just perfect," said Roussel, who was also 6-1 on faceoffs. "That was fun, obviously. I'm happy that the first one is out of the way. That's perfect to get a win, that's what's most important."
The Stars struck again 2:10 later when Dillon's slap shot appeared to deflect off defenseman Derek Morris' stick before settling just inside the right post.
"Obviously, pretty excited," the 22-year-old Dillon said. "The puck squirted out, we had a good screen in front, I saw an opening to take a shot and luckily enough, it went in. We got the win, that's the most important thing."
Vrbata got one back for the Coyotes at 14:00 when his deflection of Ekman-Larsson's wrist shot ricocheted off Jamie Benn in the crease and past Lehtonen. It was Vrbata's third goal of the season and third against Dallas.
The teams will meet again Saturday in Arizona.
NOTES: Dallas D Jamie Oleksiak, the Stars' first-round pick (No. 14) in 2011, also made his NHL debut. At 6-foot-7, the 20-year-old Oleksiak is the tallest player in franchise history. In 15:32 of ice time, Oleksiak recorded one shot on goal, one hit and one blocked shot. ... The 23-year-old Roussel is the first Stars player to score in his debut since Raymond Sawada did it on Feb. 19, 2009. ... Phoenix LW Raffi Torres served the final game of his 21-game suspension, received after his hit that knocked out Chicago's Marian Hossa in last year's playoffs. Torres, expected to play on Saturday, was initially given a 25-game ban before it was shortened to 21. He sat out 13 playoff games last spring.