Pyatt battled Bob Boughner in front for position and got to a rebound to the right of the net before hitting an open side, making it 2-0 with his eighth goal.
Defenseman Sean Hill gave Carolina some hope just over two minutes later, scoring his first goal of the season with a wrist shot from the high slot.
But Chris Taylor sealed the deal with an empty-netter, recording his third goal of the season and first in 10 games with 34 seconds left.
After two scoreless periods, Ales Kotalik gave the Sabres the lead on the power play 3:09 into the third with his ninth tally. Kotalik redirected a shot by Dmitri Kalinin past goaltender Kevin Weekes.