The Russian, 28, is seeking her third Rome title and won through 6-3 6-2 while compatriot Gavrilova, 21, beat American Christina McHale 6-2 6-4.
They meet on Saturday afternoon after Spain's Carla Suarez Navarro - conqueror of Petra Kvitova 6-3 6-2 - plays Simona Halep.
Halep thrashed her Romanian counterpart Alexandra Dulgheru 6-1 6-0.
World number three Sharapova must secure a better finish than Halep if she is to secure the number two seed position for the French Open, beginning on 19 May.
Maria Sharapova eased past Victoria Azarenka to set up an Italian Open semi-final with Daria Gavrilova.
