"That was a tremendous performance from the line of Wandell, Ott and Jamie Benn coming back into the lineup," Stars coach Marc Crawford said. "That takes pressure off the (other) lines."
James Neal scored the other goal for Dallas (5-1).
Kari Lehtonen made 28 saves and improved to 13-5-4 against Florida.
"Our goalie is playing so well," Crawford said. "He's just building such confidence from our group."
Lehtonen was 3:06 away from his fourth shutout against the Panthers when Stephen Weiss scored his first of the season.
"We had a good, solid game," Stars center Brad Richards said. "We would have liked to have given him [Lehtonen] a shutout, but we won."
Florida went 0-for-3 on the power play against Dallas, which entered with an NHL-worst 60 percent penalty-killing efficiency.
"I don't know if we can take much out of that game," Weiss said. "Just a little sloppy, a little flat-footed at times. They took advantage of the chances they got and put us away. I don't think it was for a lack of effort, but just a little static at times and it came back to bite us."
The Panthers were playing their first game since beating Tampa Bay 6-0 in their home opener on Saturday night.
"That's not an excuse, time off," Panthers coach Pete DeBoer said. "It's disappointing. Our effort, our preparation, our attention to detail, we got beat at all the things that we're supposed to be taking pride in, outworking teams and attention to detail.
"I think one through twenty, we weren't good. I don't think there's a guy in [the locker room] I could point to and say, hey, he was good."
Wandell scored his first two goals of the season in the final minute of the first and second periods.
His first goal, with 20.1 seconds remaining in the first, gave the Stars a 2-0 lead. Wandell was standing by the side of the net when the rebound of Karlis Skrastins' wrist shot from the point came right to him.
Ott had opened the scoring at 16:56 of the first period by putting home the rebound after Vokoun stopped Benn's slap shot from the wing.
Wandell's second goal, with 33.9 seconds to go in the second, was the result of an individual effort. Wandell skated around the defense and behind the net before twirling around and firing a wrist shot past Vokoun from the right faceoff dot.
"The first one was an open-netter," Wandell said. "The second one I came up with pretty good speed. A lucky break, I guess."
Florida D Jason Garrison missed the game because of a groin injury. ... Ott's goal at 16:56 of the first period ended Vokoun's shutout streak at 140 minutes, 47 seconds. ... Florida remained perfect in penalty killing this season, stopping two Dallas power plays to improve to 10-for-10. ... Richards was held without a point for the first time this season.