The win moves Nadal to within one of Roger Federer for the most Grand Slam wins by a male player in history. He also became the first man to win five Grand Slams after turning 30 in the Open Era.
Medvedev, who was looking for his first win in a major, battled back from two sets down but lost the momentum to Nadal during a tense fifth set.
Nadal is now 9-1 in Grand Slam finals when facing opponents outside of Federer and Novak Djokovic