WATCH: All Hurricanes vs. Blues highlights
"It took a good bounce and fortunately it went in," Skinner said.
Derek Ryan scored twice, Jay McClement scored, and Jordan Staal and Brock McGinn each had two assists for the Hurricanes (17-14-7). Cam Ward made 21 saves.
"It was really big," Ryan said. "It's that part of the year were points are huge. This team is really good, so obviously we wanted to have a strong game tonight and we wanted to start this two-game road trip on the right foot, and that's what we did."
Joel Edmundson and Vladimir Tarasenko scored, and Jake Allen made 25 saves for the Blues (20-14-5), who were playing for the first time since defeating the Chicago Blackhawks 4-1 in the 2017 Bridgestone NHL Winter Classic on Monday.
The Blues have gone 17 games since winning consecutive games and 21 since winning consecutively in regulation.
"I thought that was our worst game of the year," Allen said. "I don't know what you guys saw, but from everyone, we need to look at ourselves in the mirror after that game. Unfocused, [didn't execute], and just didn't play our game at all."
The Blues again allowed an early goal when Ryan scored on a 2-on-1, beating Allen from inside the left dot 1:09 into the first period for a 1-0 lead.