Liles, Eric Staal and Justin Faulk each scored during a run of three goals in a 4:36 span of the second period.
"It's a matter of all getting on the same page," Liles said, "and I think tonight we were all pretty well on the same page."
Riley Nash added a key late goal and Chris Terry had his first two NHL assists to help the Hurricanes win their second straight game and earn points in their fifth straight.
Even so, the Hurricanes remain a long shot to make the playoffs for just the second time since they won the 2006 Stanley Cup. They entered with 77 points, six behind Columbus, and with five games left, they still need a lot of help.
"It's just a matter of knowing what's successful for us, and when you have success, you can point your finger at, hey, this is why we won that game," Liles said. "Try and repeat it for the following game, and try and get on a roll. For us, it's a matter of believing in that system and that reason why we've been winning games, and we've been coming out on the right end of it."
Carolina has the league's second-worst power play but scored twice with the man advantage.
"You take a couple penalties, they score back to back on power plays and anytime that happens, it's not a good thing," defenseman Alex Goligoski said. "We got behind the 8-ball there, got a push at the end of the second, but when you get down 3-0, it's tough."
Anton Khudobin made 33 saves in Carolina's first win over the Stars since 2009.
"I had a couple saves, and we just started playing (well) and got the result," Khudobin said.
Tyler Seguin scored for Dallas, which entered occupying the Western Conference's last wild-card spot but had its three-game winning streak snapped. The Stars were coming off a 5-0 pounding of Washington and had won five of six.
Kari Lehtonen made 13 saves but was pulled after allowing three goals. Tim Thomas took over and finished with 15 stops.
Seguin pulled the Stars to 3-1 by beating Khudobin high to his glove side at 9:44 of the second. But Khudobin made the save of the night roughly 30 seconds into the third when he slid across the net to stop Alex Chiasson.
"We could have been right back in the game," Dallas coach Lindy Ruff said. "We didn't finish."
Nash then restored the Hurricanes' three-goal lead when he blasted a rebound past Thomas with 12:20 left.
Carolina skated in this one without forwards Alexander Semin, who was out with an illness, and Jiri Tlusty, who has an upper-body injury.
And their offensive flurry started with a fluke.
Liles -- who had his first three-point night since 2011 -- fired a shot that richocheted off Staal's left skate, popped high into the air and fluttered behind Lehtonen at 2:30 of the second. That gave the Carolina captain goals in consecutive games but just his third since March 1.
"We always say, `Shoot the puck," Hurricanes coach Kirk Muller said. "This time of year, it doesn't have to be highlight goals. Just get it there and you never know what's going to happen."
There wasn't anything cheap about the Hurricanes' second goal: Faulk took a feed from Liles behind the left circle and blistered the puck past Lehtonen at 4:08.
Liles capped his first multi-point game since coming to Carolina in a New Year's Day trade with Toronto by beating Lehtonen with a quick wrist shot from the left circle to make it 3-0 at 7:05.
"I wouldn't say that I've been playing bad hockey -- I think that I've been contributing," Liles said. "Maybe the points aren't there. ... You play in the league long enough, it's going to happen."
Seguin has points in seven of his last eight road games. ... The Hurricanes recalled Zach Boychuk from their AHL affiliate in Charlotte to help replace Semin and Tlusty. ... D Andrej Sekera (lower body) was a late scratch for Carolina. ... Dallas LW Ray Whitney suffered a lower-body injury in the first period and did not return.
Copyright by STATS LLC and The Associated Press
RALEIGH, NC - APRIL 03: John-Michael Liles #26 of the Carolina Hurricanes carries the puck through the neutral...