Medvedev, who had not won a match in three previous appearances in Rome, levelled the scores before Rune broke again for a 4-3 advantage.
The 20-year-old bounced back strongly at the start of the second, breaking Medvedev's opening serve and holding to take a 2-0 lead. After the start of the final was delayed by nearly two hours, both players held serve through a tight first 11 games, but Medvedev took advantage of a poor drop shot from the Dane to claim the first set 7-5.
