The front-row duo went over in the first half and their efforts, in addition to a second-period penalty try, proved enough for the Azzurri to open their autumn schedule with a hard-fought victory.
Cittadini put Italy in front after six minutes but Tonga prop Sona Taumalolo responded for the visitors shortly after the half-hour mark.
Ghiraldini restored the hosts' advantage on the stroke of half-time and a penalty try, converted by Kris Burton, saw them extend their lead to 12 points
Tonga came again and Fetu'u Vainikolo went over after latching on to a diagonal kick with 13 minutes to go but Italy held on.
Italy coach Jacques Brunel will demand better from his side, however, ahead of trickier assignments against New Zealand and Australia.