The most dizzying sequence started when Skinner broke a 2-all tie by pushing a wraparound past Enroth's left pad with 6:04 left.
The Hurricanes won the ensuing draw, and Eric Staal slipped through the Buffalo defense and beat Enroth with a backhand at 5:55 to make it 4-2 and cap a frenetic period in which the teams combined for six goals.
"You've got to get big saves on those plays or they end up hurting you," Sabres coach Lindy Ruff said, "and that one really hurt us."
Skinner gave Carolina its first lead of the season 62 seconds into the second with a tricky backhand over Enroth's left shoulder. Faulk then made it 2-0 with 15:54 left when he stormed down the ice on a short-handed 3-on-1 rush and blasted a slap shot by Enroth.
Then it was the Sabres' turn to get the offense going.
Hodgson pulled Buffalo within a goal at 11:10 by beating Ward with a backhand of a loose rebound, and Pominville tied it at 2 with 9:21 left with a redirection of Christian Ehrhoff's slap shot.
"I think we gave up the puck too much," Pominville said. "We battled back a couple of times . (but) we gave up too many rush opportunities and were a little too casual with the puck. It just wasn't our usual game."
NOTES: Skinner finished with his eighth career multigoal game. . The teams play again Friday night in Buffalo. . The Hurricanes' record for quickest two goals came in 1987 when Sylvain Turgeon scored twice in 6 seconds. . Buffalo didn't put a shot on goal until LW Marcus Foligno's backhand roughly 7½ minutes in.