All three of the tournament's top seeds have been eliminated.
Pennetta took control with consistent and accurate groundstrokes, along with a more effective serve. She had 19 winners compared to 12 for her Australian opponent.
"It's a good feeling because she's one of the best players," Pennetta said. "She has had an unbelievable year. It's never easy to beat this kind of player. For me, it's much better to play against her."
Pennetta, the No. 5 seed from Italy, will meet Russia's Svetlana Kuznetsova in the semifinals. The unseeded Kuznetsova ended the run of local teenager CoCo Vandeweghe 7-5, 6-2.
"I think I won by experience," said Kuznetsova, who reached her first semifinal this season. "I wasn't playing my best game. I think she was so confident (Thursday). It took me time to break her up."
In a match of unseeded players, Slovakia's Daniela Hantuchova eliminated Alisa Kleybanova of Russia, 2-6, 6-4, 6-3 to reach the semifinals. Hantuchova will play No. 4 seed Agnieszka Radwanska of Poland, who won the last nine games to rout seventh-seeded Shahar Peer of Israel, 6-2, 6-0 in a Friday night match.
Pennetta has beaten Stosur, ranked No. 5 in the world, in their three career meetings — including twice this year.
Stosur, the French Open runner-up this year, didn't record an ace and had five double-faults. Stosur is considered to be the second-best server behind No. 1 ranked Serena Williams. Pennetta had eight aces and one double-fault.
"I can return her kick serve. There are few shots that I have that can make her nervous all the time," Pennetta said. "She's one of the best servers. I am really comfortable with her ball. I can handle the speed."
Pennetta has 13 career wins over a top 10 player, but it was her first since the 2009 U.S. Open.
"She makes a lot of balls and runs everything down," Stosur said. "She really makes you work for every point you win. Sometimes that can be a little bit frustrating."
Vandeweghe, the 18-year-old player who grew up about 10 miles from the tournament location, seemed to carry the momentum she had from Thursday night's three-set upset win over Wimbledon finalist Vera Zvonareva.
Vandeweghe, who had to win three matches in the qualifying tournament to get into the main draw, took a 5-2 lead in the first set against the struggling Kuznetsova.
"I thought early on I was kind of beating her with my pace and the heaviness of the ball," she said.
But the two-time Grand Slam titlist turned it around when she saved one set point in the eighth game. Kuznetsova won five consecutive games to take the set.
"It's hard when you go on the court and you have no clue how a girl will play," said Kuznetsova, who faced Vandeweghe for the first time. "I was trying to adjust to her game. At some moment I started to understand a little bit more how she plays. I understood what she doesn't like, what she likes and tried to mix it up so she couldn't hurt me."
At 1-all in the second set, Kuznetsova rolled through four straight games to go ahead 5-1. The Russian finally put away the 205th-ranked Vandeweghe on her third match point in the eighth game.
"I came in a little bit tired from last night, a little heavy legged," said Vandeweghe, who said she has received a wild-card entry to play next week at Cincinnati. "I had a great first set. She's a two-time Grand Slam champion for a reason."
Vandeweghe is the niece of former NBA star Kiki Vandeweghe, who also served as the New Jersey Nets' general manager and coach. Her grandfather, Ernie, played for the New York Knicks in the 1950s.