The 11th-ranked Pennetta used her consistent baseline game to wear down the 132nd-ranked Glatch, breaking early in the first set to set the tone, then cruising in the second set.
Francesa Schiavone of Italy faced U.S. Open quarterfinalist Melanie Oudin in the second singles on the outdoor clay court at the Rocco Polimeni club.
Reverse singles and doubles are slated for Sunday in the best-of-five series.
The United States is without both Serena and Venus Williams, who opted not to play after meeting in the season-ending tour championships final last weekend.
Glatch routed Pennetta 6-1, 6-1 in the first round of this year's French Open, but she was never in control this time on a cool and overcast day in southern Italy.
Glatch managed to break Pennetta in the opening game of the second set but then the Italian took control.
Pennetta finished with 33 winners to Glatch's 14 and broke the 20-year-old American five times.