Ryan Suter had two assists, and Jake Oettinger made 27 saves for the Stars (24-11-6), who avoided losing three in a row for the first time this season.
"Real slow start. I thought our energy wasn't great," Dallas coach Peter DeBoer said. "I think that last [road trip from Jan. 3-4], getting back really late, I think we carried that a little bit into the first period.
"[Oettinger] was our best player, that's exactly the story. The goalie gave us a chance to get our legs under us. We got some timely goals, and we won the special teams battle, which is critical and a big piece of what we've done all year."
Carter Verhaeghe scored, and Spencer Knight made 29 saves for the Panthers (18-19-4), who failed to win their third straight for the first time this season.
"Our effort was there," Florida captain Aleksander Barkov said. "I think the first and second period, we played well enough to maybe come out with the lead after the second period. I feel like they've just got the goals and the confidence, and then they shut it down in the third period."
Robertson gave Dallas a 1-0 lead at 16:45 of the first period, scoring on his own rebound from a sharp angle.
"Definitely want to get the first goal in every game, especially when we're kind of on our heels," Robertson said. "[We] kind of slowed down their momentum and tried to take over in the second and third period."
Nils Lundkvist extended the lead to 2-0 at 10:03 of the second period with a one-timer from the top of the left face-off circle on a power play.
"Obviously, you don't want a ton of Grade A's [against], but sometimes you need to be sharp early and let the guys find their legs," Oettinger said. "After that first period, where they were great, we were the better team and our guys scored some big goals. It's fun to win at home."