Adam Boqvist and Patrick Kane each had two assists for the Blackhawks (14-9-5), who scored four goals on 16 shots.
Chicago split the two-game set in Dallas after a 6-1 loss Tuesday.
"It was a big win, an important win," Blackhawks coach Jeremy Colliton said. "We knew they were going to be a desperate team again. It certainly wasn't perfect, but I thought we found ways to defend. Obviously, the special teams were big for us, and [Lankinen] made a couple saves early, especially in the first period, that allowed us to take control of the game."
Roope Hintz and John Klingberg scored for the Stars (8-9-5), who were 2-0-1 in their previous three games. Anton Khudobin allowed four goals on eight shots through the second period and was replaced by Jake Oettinger, who made eight saves and got his first NHL assist.
"The power play was awful, the penalty kill wasn't good enough," Dallas coach Rick Bowness said. "When you're off like that, you would hope your power play would get you a goal to get you going. It didn't happen tonight. Again, [the Blackhawks] had two even-strength shots on net after 40 minutes. The good things we're doing are getting lost because we're not scoring on the chances that we had, and the special teams clearly were the difference tonight."
Chicago was 5-for-5 on the penalty kill, including killing a 35-second 5-on-3 opportunity beginning at 18:35 of the second period.
"It probably wasn't our best game, but we got the two points, so we need to take the positives," Blackhawks defenseman Duncan Keith said. "Our power play was good (2-for-5), I thought our penalty kill did a really good job, especially on that 5-on-3 killing it."
Dominik Kubalik received a backhand pass from Brandon Hagel and shot between Khudobin's legs for a 1-0 lead at 5:26 of the first period.