A good spell of early pressure from Capri paid off after a scramble in the box resulted in the ball landing at the feet of Gaetano Letizia, who rifled the ball home from seven yards out after some good work from Marco Borriello.
Mattia Destro had an excellent chance for the visitors moments before half time when the Italian international met a low cross but his strike was directed straight at the goalkeeper.
Anthony Mounier was presented with a chance just moments later from six yards out but the Frenchman could not turn the ball home.
Giaccherini had another free kick from a difficult angle well stopped by Belec as the Italian looked to fool the Capri goalkeeper from the set piece.
The away side finally made the breakthrough in added time as Adam Masina, with the club since the age of 13, scored after the goalkeeper palmed the ball into his path and the 21-year-old gratefully accepted the gift.
The win lifts Bologna off the bottom of theSerie A table, while Carpi replace them at the foot of the standings.