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.
Francesca Schiavone 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 were scheduled 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.
"She definitely played better than last time," Glatch said. "The conditions were also different. It was much quicker and hot that day and very dry, and I served extremely well. I was more aggressive in that match, and I probably should have tried to be in this match."
Glatch managed to break Pennetta in the opening game of the second set but then the Italian took control.
"After I broke her, the next two games she really stepped it up," Glatch said. "She hit a couple great shots."
Pennetta finished with 33 winners to Glatch's 14 and broke the 20-year-old American five times. Glatch struggled with her mobility, watching several winners whizz by her within reach.
"She has a pretty varied game," Pennetta said. "She can slice the ball, hit it hard, topspin. You need to move her around because once she starts moving she has trouble."
The 6-foot Glatch likes to rely on her serve, but she won only won 43 percent of the points on her first serve.
"My serve kind of let me down," she said. "I didn't win a lot free points off my serve, so it made it very difficult to hold serve."
One of the few things Pennetta struggled with were low balls, with the heavy clay hardly providing any bounce.
"There was a bit too much clay on the court but that's what we asked for," Pennetta said.
