The Spanish qualifier recovered from losing a tightly contested opening set to complete the victory in two hours and 58 minutes at the Ariake Coliseum.
Fritz, the 2022 Japan Open champion and world No. 12, edged the first set through a tie-break after neither player was able to establish a decisive advantage.
Munar responded strongly in the second set, breaking Fritz in the ninth game before serving out to level the match at one set apiece.
The 29-year-old Spaniard then took control of the deciding set, securing two breaks before closing out the biggest win of his Tokyo campaign.
Munar also benefited from Fritz struggling physically during the contest, with the American requiring a medical timeout for a left-thigh problem.
The victory is Munar's third win of the season against a player ranked inside the world's top 20, according to reports from Tokyo.
Munar, who entered the main draw through qualifying, will face Portugal's Jaime Faria in the last 16. Faria advanced after beating Britain's Arthur Fery 6–4, 3–6, 6–4.
• Jaume Munar: defeated Taylor Fritz 6–7(7), 6–4, 6–3
• Taylor Fritz: eliminated in the first round
• Next opponent: Jaime Faria
• Tournament: Kinoshita Group Japan Open
• Category: ATP 500
• Venue: Ariake Coliseum, Tokyo