Rune, ranked ninth in the world, went into the match as big favorite against the Frenchman, who is ranked 40th in the world.
The 22-year-old Dane took the lead against Müller, who is six years older, after just a few minutes of the match.
Alexandre Müller did manage to win his first service game but then Rune showed his quality by breaking Müller's serve twice in the first set.
The second set went much like the first, when Holger Rune quickly broke his opponent's serve to take a 2-1 lead. And from then on, the Dane never looked back and did not allow Müller back into the match.
It was the second time in his career that Rune defeated Muller. The two players also met four years ago in a challenger tournament in Italy, where Rune also took the win in the end.
In the fourth round, Holger Rune will face Alexei Popyrin, who is ranked 26th in the world.
The Australian surprisingly beat Russian Daniil Medvedev 5-7, 6-4, 6-4 on Friday morning CET.
Rune won his last meeting against the 25-year-old Popyrin in three sets on clay in Rome two years ago.