Medvedev came within two points of defeat before finally advancing with a 5-7, 7-6(4), 6-3 victory over Korda after a battle that lasted for two hours and 23 minutes.
The World No.2 defeated Poland's Magda Linette 6-4, 3-6, 6-3 in a match that lasted for two hours and 9 minutes to book her place in the third round of the tournament.