The top-seeded Li never trailed in a routine 63 63 defeat of eighth-seeded Bojana Jovanovski.
"I was a bit too eager to win and became a bit anxious when I didn't serve well," said Li, who had 10 double faults. "But I am satisfied with my performance today."
No.6 seed Peng had a much tougher time of it, saving a match point down 62 54 against 18-year-old German Annika Beck before eventually pulling out a 26 75 62 triumph.
"Annika came out so strong and played so well the whole match," Peng said. "Even in the second set, I was behind almost the whole time, but the fans kept cheering me on, and like in all my matches, they gave me the encouragement and support I needed to win."
Among Li's feats are becoming the first Asian to win a Grand Slam title at the 2011 French Open, after which she tied Kimiko Date-Krumm as the highest-ranked Asian by rising to No.4. Peng became China's second-highest-ranked player ever after Li when she climbed to No.14 in August 2011.
"It's good to have the opportunity to play a player from my home country," said Li, who is 4-1 against Peng. "It's a new challenge. If I can deal with this well, the experience will help me with other matches."
Friday's other semifinal will see fifth-seeded Klara Zakopalova take on Monica Niculescu. Zakopalova had a surprisingly easy time with second-seeded Marion Bartoli, 63 62, only losing two more games the rest of the way after getting in an early 3-1 hole.
"It was very windy today," Zakopalova said. "It wasn't just about tennis. It was more about thinking positive and fighting for every point."
Zakopalova has had some success against the Frenchwoman in the past, and is now 3-3 in the series.
"Klara played very well," Bartoli said. "She has beaten me in the past outdoors. I think her game disturbs me more outdoors than indoors. It was also very windy today, so I had trouble addressing the ball and was uncomfortable. I started really well, 3-1, and lost a couple tough games and then she regained some confidence."
Niculescu used her trademark slice forehand to dispose of Chinese lucky loser Zhou Yi-Miao, 64 62.
"I've never played against Niculescu," Zakopalova said. "For sure it will be a tough match. She moves very well, she fights, and she plays with a slice forehand. She's really the only player who does that."