The Gulls went in front eight minutes before half-time when full-back Chris Robertson crossed in for Carayol and, at the second attempt, the youngster rifled home on the turn from 12 yards.
After the restart, Lee Mansell came close to doubling Torquay's lead, before Bury nearly hit back with skipper Stephen Dawson heading over the crossbar from just eight yards.
With Bury pushing desperately for an equaliser, Torquay completed a fine victory - their fifth in a row - with two late breakaway goals.
With three minutes left on the clock, substitute Danny Stevens latched onto Nicky Wroe's pass before firing home low into the corner from 15 yards.
Then, in stoppage time, striker Scott Rendell also fired into the corner after being neatly teed up by Stevens.