Liles set up scores from Eric Staal and Justin Faulk that staked the Hurricanes to a 2-0 advantage before adding a power-play tally later in the middle session.
Anton Khudobin made the lead stand with a sharp 33-save effort in Carolina's second impressive win in three days. The Hurricanes returned home off Tuesday's 4-1 road decision over Metropolitan Division leader Pittsburgh.
Dallas, which came in having outscored the opposition 16-5 in winning its last three, remained tied with Phoenix for the final playoff spot in the Western Conference. The Stars do have a game in hand on the Coyotes.
Tyler Seguin had Dallas' lone goal. Stars netminder Kari Lehtonen was pulled midway through the second period after letting up three goals on 16 shots, with Tim Thomas stopping 15-of-16 chances in relief.