Liles, Eric Staal and Justin Faulk each scored during a run of three goals in a 4:36 span of the second period.
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. Carolina has the league's second-worst power play but scored twice with the man advantage.
Anton Khudobin made 33 saves to help Carolina beat Dallas for the first time since 2009.
Tyler Seguin scored for Dallas, which entered occupying the Western Conference's last wild-card spot but had its three-game winning streak snapped.
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. Nash then restored the Hurricanes' three-goal lead when he blasted a rebound past Thomas with 12:20 left in the third.
The Stars — who were coming off a 5-0 pounding of Washington and had won five of six — fell too far behind a Carolina team that may have once again figured things out too late.
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 need a lot of help with five games left.
They 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.
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.
NOTES: 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.
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