Perkins also grabbed 12 rebounds as the Celtics ran their winning streak to five straight games. Kevin Garnett added 16 points, including four during a 9-2, first-quarter run that put Boston up 27-12.
The Celtics never looked back and won for the 15th time in 20 games against the Bobcats.
Allen hit a 3-pointer at the first-half buzzer, pushing the Celtics to a hefty 62-39 lead going into the locker room.
Charlotte's four-game winning streak was snapped by the loss. The Bobcats were led by Nazr Mohammed's 16 points, while Raymond Felton had 14 and Boris Diaw 13 in the loss.