Kari Lehtonen made 18 saves as Dallas (22-20-8) won for the second time in its last 11 games. It was his second shutout of the season and No. 24 for his career.
Dallas was coming off a 4-1 loss at Nashville on Monday night, while the Wild played for the first time since a 3-2 overtime victory over the Stars on Saturday.
Minnesota (27-20-5) dropped to 7-3 in 2014.
Most of the first period was played in the Minnesota end. Dallas finished with 12 shots on goal to only three for the Wild. The Stars also had all three power plays in the first.
"This game goes in the garbage," Wild coach Mike Yeo said. "We didn't execute. We didn't defend. We were passengers. We were spectators through the whole game."
"We won the opening faceoff and we spent 40 seconds in our own zone," Yeo said. "That's a bad sign right there that we weren't ready to execute. It just trickled on from there."
Dallas scored at 13:18 of the first when Vernon Fiddler sent a wobbly drive from the top of the left faceoff circle over Kuemper for his first goal in 28 games.
The Stars then added to their lead by scoring a power-play goal for the fifth consecutive game. Cole put the puck in the upper right corner from the left circle at 16:45, with Alex Goligoski earning his second assist of the game.
"It's a tough game when you're chasing," Wild centre Kyle Brodziak said. "Being down 2-0 early on like we were, you feel like the rest of the game you're chasing the game. It's a tough league to be doing that. Good teams know how to shut you down. We couldn't get anything going."
The final goal was on a third-period penalty shot by Benn. Not Jamie Benn, the team's second-leading scorer, but Jordie. The defenceman entered the game with two career goals.
Jordie Benn skated in on Kuemper, got him to move to his left and slipped a backhand shot past him.
Benn said he had taken a penalty shot once before in the minors.
"I did that exact move, and it worked," he said. "That's the only move I have, the only one I've ever tried, and it worked again."
Jamie Benn joked: "I pretty much taught him everything he knows."
Stars coach Lindy Ruff had a different perspective.
"I think that's a move Jordie should teach Jamie. I'm serious," he said. "That was a solid pump fake."
Whitney got on the board at 13:18 of the second period, lifting the Stars to a 3-0 lead just two seconds before a high-sticking penalty on Minnesota's Justin Fontaine ran out.
Sergei Gonchar skated toward the net, and then passed to Whitney. He pulled the puck away from Kuemper, and then pushed it behind him. The shot crossed the goal line before a Wild defenceman could knock the puck away.
It marked the Stars' fourth game this season with two power-play goals.
"The third goal was huge," Lehtonen said. "It settled things even more, and made it less stressful for me."
Dallas outshot Minnesota 16-6 in the second period, and 36-18 for the game.
NOTES: Cole scored two goals in this season's first 25 games, but has 12 since the slow start - including three in his last five games. ... Dallas had 20 power-play goals in its first 45 games. The Stars have six in the last five games, and have improved from 29th to 27th in the NHL with a man advantage. ... Whitney's power-play goal was Dallas' 10th at home this season, inching the Stars toward an 11-per cent success. They still rank last in the league on home power plays. ... Minnesota was 0 for 2 with a man advantage, extending its current drought to 0 for 14. ... Dallas is 4 of 7 on penalty shots this season.