Radwanska, who held a 6-2, 3-0 lead when her match resumed on Court Suzanne Lenglen, lost 10 consecutive games to put herself in deep trouble.
She asked for a medical timeout after the third game of the decider to receive treatment on her right forearm and hand. It didn't have an immediate effect as she dropped her serve at love in the next game.
Radwanska finally managed to stop the downhill spiral when she broke in the fifth game but could not stop Pironkova from advancing to the quarterfinals.
The players were pulled off court Sunday evening because of rain and darkness and could not play Monday when the entire day was washed out for the first time in 16 years.
Pironkova advanced to her third career Grand Slam quarterfinal after reaching the semifinals at Wimbledon in 2010 and making it to quarters at the All England Club the next year.
Stosur was the 2011 US Open champion and a finalist at Roland Garros in 2010.
The Associated Press contributed to this report.