Skinner opened the scoring in the second and set up Justin Williams' goal 1:09 into the third.
Williams scored his first of the season on the power play when he got the puck near the faceoff dot and, as goalie Mike Smith stacked his pads, the veteran put a shot under the crossbar.
Sean Monahan scored for Calgary.
Carolina improved to 3-1-1 overall and 2-1-0 on a four-game trip.
Also assisting on the play was Jaromir Jagr. The 45-year-old, still looking for his first goal with Calgary, also was the victim on one of Darling's best saves. In third period, Darling threw up his glove to stab Jagr's dangerous chance from just a few feet away.
In a scary incident halfway through the first period, Skinner hit veteran Kris Versteeg twice in a row with shots. First, he hit him in the knee. Just a few seconds later while Versteeg was down on the ice, writhing in pain, Skinner's slap shot appeared to hit him in the helmet.
Versteeg had to be carried off the ice, but Versteeg returned early on in the second.
Carolina scored once on six power, plays while the Flames were scoreless on their lone attempt. ... For the first time in his four games, Jagr played right wing on the Flames' top line with Monahan and Gaudreau. ... Carolina defenceman Trevor van Riemsdyk (concussion) returned after missing three games.
Hurricanes: At Dallas on Saturday night.
Flames: Host Minnesota on Saturday night.
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