Pavlyuchenkova, the world number 32, won 6-7 (2/7), 6-2, 9-7 and will face 85th-ranked Tamara Zidansek of Slovenia for a place in the final.
"There are so many emotions to reach a Grand Slam semi-final for the first time," said 29-year-old Pavlyunchenkova who had fallen at the quarter-final stage at the majors on six previous occasions since her 2007 debut.
"It's tough to play against your friend."
She added: "I always had the tennis. Mentally I'm probably more solid now. Just trying to play smarter tennis. I'm working harder."
Rybakina, who had knocked out Serena Williams in the previous round, raced into a 4-1 lead in the opener against a player who had also made the quarter-finals in Paris in 2011.
Pavlyuchenkova broke back in the seventh game before the 6ft (1.84m) Russian-born Kazakh raced confidently through the tiebreak.
The Russian levelled the tie courtesy of breaks in the sixth and eighth games of the second set.
In a tense decider, there were four breaks in the first six games before Rybakina cracked in the 16th game, going down tamely on her sixth double fault.