Glatch lost to Flavia Pennetta 6-3, 6-1, and Francesca Schiavone rallied after a two-hour rain delay to defeat Oudin 7-6 (2), 6-2 on the outdoor red clay court at the Rocco Polimeni club.
Reverse singles and doubles were scheduled for Sunday in the best-of-five series.
The U.S. has won all nine of its previous meetings with Italy. But the Americans are without Serena and Venus Williams, who opted not to play after meeting in the season-ending tour championships last weekend in Doha, Qatar.
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.
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," Glatch said. "I didn't win a lot free points off my serve, so it made it very difficult to hold serve."
Oudin, who reached the quarterfinals of the U.S. Open, took a 4-2 lead with an early break in the first set before a nearly two-hour rain delay. Schiavone broke back in the first game when play resumed, using a drop-shot winner on her first break point.
With the crowd chanting "Fran-CES-ca, Fran-CES-ca" between points, the 18-year-old Oudin maintained her concentration and saved three break points to take a 5-4 lead. She flattened out her forehand for a couple of winners up the line and used an effective drop shot of her own on occasion, yelling "C'mon" whenever she won a big point.
In the tiebreaker, Schiavone's bigger serve and more powerful groundstrokes made the difference, and the Italian landed an inside-out backhand return winner on the line on her first set point.
Oudin broke in the opening game of the second set but Schiavone broke right back and took a 5-1 lead against the teenager from Marietta, Ga. Schiavone then dropped her serve, but broke in the next game to close it out when Oudin landed a forehand in the net.
Glatch routed Pennetta 6-1, 6-1 in the first round of this year's French Open, but she was never in control on the slow clay during 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."
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