Fritz, the highest-seeded American in the draw beat Alejandro Davidovich Fokina (23) 7-5 6-2 on the back of a decent first serve despite trailing by a break in the opening set.
Fritz hit only 11 winners to the Spaniard's 20 but he converted five break points to wrap up the match in 90 minutes to beat Davidovich Fokina for the first time in three meetings.
"Really happy, he's a tough person to play against. 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.
"He makes a lot of crazy shots and he's beaten me the past two times."
Fritz needs to reach the final to have any chance of sealing a place in the ATP Finals in Turin ahead of Andrey Rublev (25) or Felix Auger-Aliassime (22), who has won his last three tournaments.
"Turin is still in the picture, obviously, but there's not much else I really could have done. I won Tokyo," he added.
"Felix has played really, really well, so he deserves it, but I am going to try to steal his spot this week for sure."
Fellow American John Isner (37) can remove one hurdle in the form of Rublev after he booked a place in the second round against the Russian with a 6-4 7-6(3) win over Germany's Oscar Otte (29).
The towering Isner, who finished runner-up to Andy Murray in 2016, fired 19 aces in the contest to wrap things up in 82 minutes.
Frances Tiafoe (24) also moved into the second round without conceding a break point with a 6-4 6-4 win over Lorenzo Sonego (27) while fellow American Maxime Cressy (25) ousted Argentine Diego Schwartzman (30) 6-3 6-3.
In a mixed day for the Italians, Lorenzo Musetti (20) beat Marin Cilic (34) in straight sets to advance but 11th seed Jannik Sinner (21) was knocked out by Swiss qualifier Marc-Andrea Huesler (27) who is ranked 49 places below him.
Defending champion Novak Djokovic (35), world number one Carlos Alcaraz (19), Rafa Nadal (35) and Daniil Medvedev are among the main seeds who received a bye into the second round.
