Rune on Wednesday night booked his ticket for the third round of the French Open after a three-set victory over American wildcard Nava.
Rune had the luxury of playing his second-round match on the largest arena at the French Open, Court Philippe-Chatrier, and the Dane lived up to the prestigious surroundings.
Rune delivered a solid and composed performance and won in three sets, 6-3, 7-6, 6-3, against Nava, who is ranked 137 in the world.
The Dane served well throughout the match, his baseline play was outstanding and he spiced up his game with several distinguished winners.
Rune is thus ready for the third round, where Frenchman Quentin Halys awaits. The home-court favourite is ranked 52 in the world.
On paper, Rune was a big favourite against the underdog Nava, but the American looked like a player who should be significantly higher in the world rankings for large periods of the game.
But Rune still managed to get through the match without conceding a set and afterwards, the Dane was naturally relieved in his on-court interview with former French star Alize Cornet.
"I think it went well today. I played really well in the first set, while the second set was a big challenge where I had to dig deep and find some big shots. I had to be consistent because he played really good tennis.
"In the third set I also started really well, but I lost a little bit of focus. I came back though, so I'm really happy."