Andrej Sekera added two assists for Carolina, which scored three goals in the second period while going up 4-0.
Jake McCabe scored the Sabres' goal.
Lindholm, Carolina's first-round pick in 2013, scored his first goal by whipping a rebound past Neuvirth to make it 2-0 at 3:46 of the second, moments before Skinner's one-timer from Gerbe.
Lindholm's second goal came with 9:57 left in the second and made it 4-0. He completed the hat trick by scoring into an empty net with 3:56 left.