Radulov had four points, Joe Pavelski and Tyler Seguin each had a goal and an assist, and Roope Hintz scored for Dallas (5-8-1), which trailed 3-0 late in the second period. The Stars finished a four-game homestand 3-1-0 after a 2-7-1 start.
"We don't want to give up, and that's the bottom line," Radulov said. "We heard our fans weren't happy and we weren't happy with the two periods, even though I think the first wasn't as bad as the second. At the end of the second, we did a lot of good things.
"It's good to have a comeback, but it's hard to fall down 3-0, especially at home."
WATCH: [All Wild at Stars highlights]
Ben Bishop was pulled after the first period; he allowed two goals on 10 shots. Anton Khudobin made 11 saves in relief.
"We just thought [Bishop] wasn't on top of his game, that's all," Stars coach Jim Montgomery said.
Eric Staal and Jason Zucker each had a goal and an assist, and Ryan Suter scored for Minnesota (4-8-0). Alex Stalock made 31 saves.
"Momentum is real," Staal said. "Momentum in games is real. We had all of it, and then it shifted. I don't know what the answer is as to why, but we've got to figure that out. It obviously helped them the other way."
Radulov started the rally when he scored while falling down in the slot at 19:12 of the second period to make it 3-1.