Under overcast skies, the World No 11 quickly imposed herself and broke Glatch to go 2-1 up thanks in part to a superb drop shot.
She then sealed the first set when Glatch was broken again after going long on the red clay in the southern Italian town of Reggio Calabria.
Pennetta lost focus slightly at the start of the second set, being broken in the first game, but stormed straight back with a graceful winner to level at 1-1 and easily wrapped up the match.
Melanie Oudin, the top-ranked American after Serena and Venus Williams, who decided not to compete, faces Francesca Schiavone in the second singles rubber later on Saturday.
Rain is forecast for Sunday when the reverse singles and doubles match are scheduled. Organisers have the option of extending play until Monday if the tie is not completed.
Sania sent packing by Schiavone at Japan Open
Pennetta whitewashes Sania to enter third round
Meet the Cinderella from Georgia
Venus and Serena Williams win US doubles crown
Petrova strolls, Pennetta struggles