Fritz, the highest-seeded American in the draw beat Alejandro Davidovich Fokina 7-5 6-2 on the back of a decent first serve despite trailing by a break in the opening set.
He's got weapons on both sides, he's extremely quick as well, so there's nowhere you can really play with a lot of safety," Fritz said.
"Felix has played really, really well, so he deserves it, but I am going to try to steal his spot this week for sure."
Frances Tiafoe also moved into the second round without conceding a break point with a 6-4 6-4 win over Lorenzo Sonego while fellow American Maxime Cressy ousted Argentine Diego Schwartzman 6-3 6-3.
Defending champion Novak Djokovic, world number one Carlos Alcaraz, Rafa Nadal and Daniil Medvedev are among the main seeds who received a bye into the second round.