Cam Ward turned away 41 shots in regulation and overtime and denied all three attempts during the shootout to grab the victory for the Hurricanes, who got the game-tying goal in the second period from Finnish winger Tuomo Ruutu in the second period.
Andrew Brunette scored the lone goal for the Wild, who received 36 saves in defeat from Helsinki native Niklas Backstrom.
Skinner, the seventh overall selection in the 2010 NHL Entry Draft, started the shootout with a backhand-to-forehand move and deposited a wrist shot over a sprawling Backstrom to become the third-youngest player ever to score a goal in the six-year history of the format.
Ward then stopped Mikko Koivu and Brent Burns before moving left to right to deny Antti Miettinen to sew up the victory.
The Carolina netminder Ward made saves on three Koivu thrusts from in close in the first half of the opening period, but the Wild got on the board with just over 2 1/2 minutes left in the opening period on a power-play tally.
Cam Barker made his way toward the net from the blueline and then dished off to Koivu, who fired from the slot and Brunette was there to put home the rebound unimpeded from the left doorstep.
Then early in the second period, Skinner came down the left side and from just inside the top of the circle poked the puck past Backstrom, who came out of the net to challenge. Jussi Jokinen got the disc behind the net on the other side and sent a backhand pass to Ruutu, who wristed a one-timer past Backstrom two minutes in.
Carolina killed off 5 1/2 minutes of short-handed time, including 30 seconds of a two-man disadvantage, to keep the game even with four minutes left in the middle session.
Later in the period, Martin Havlat took a backhand feed from behind the net and sent a shot from the slot that was initially turned away by Ward on a left pad save. The play was then reviewed to see if the puck had crossed the goal line before the save, but the call on the ice was upheld.
Minnesota killed off a two-man disadvantage 12 1/2 minutes into the third period and then missed a chance to regain the lead when Havlat shot just wide on a breakaway with 2 1/2 minutes to go in the game.
Carolina went back on the power play a minute later but could not capitalize at the end of regulation and into the extra session.
Havlat was sprung on another breakaway and hit the right post over a sliding Ward, and was denied again from in front on a delayed penalty call. The Czech winger was slashed on the initial attempt that resulted in a power play with only seven seconds remaining in the extra session.
Carolina defeated the Wild for a seventh time in 13 all-time meetings…Ward is 3-0-1 in five career meetings against Minnesota, while Backstrom is 3-2-1 versus the ’Canes…This was the first of 21 back-to-back games for Carolina, while Minnesota will play on consecutive nights 19 times.