It was the 17th seed's second-straight win over the German after his victory at Indian Wells earlier this month.
Zverev crushed an ace to capture the first set but Fils turned the tables in the second, securing an early break and smacking a cross-court winner to level the contest.
Zverev broke for a 3-1 lead in the decider but then began to struggle with his accuracy as his normally trusty backhand failed him at critical moments while his opponent began to feed off the energy of the crowd.
Fils, 20, confidently served out the match to set up a quarter-final showdown with 19-year-old Jakub Mensik of the Czech Republic.
"In the third set I thought it was over almost, 3-1, he's serving great," Fils said after the match, which had been postponed a day due to rain.
"But I said don't get mad, just try to play as much as you can, try to fight and if you make a break, it's nice. And it happened."
In the day's other quarter-final, cramping 14th-seed Grigor Dimitrov barely survived the oppressive humidity to outlast No.23 seed Francisco Cerundolo 6-7 (8-6) 6-4 7-6 (7-3) in a nearly three-hour battle.
Dimitrov was led off the court by a tournament doctor and ATP physio after sitting in his chair for over 25 minutes, saying he was feeling "dizzy."
Dimitrov, a Miami Open finalist in 2024, saved a match point in the third set when trailing 5-6 before forcing a tiebreaker. He squandered seven set points in the opening set and lost the tiebreaker 6-4.
He will next face the winner of Novak Djokovic and Sebastian Korda, whose clash was pushed to Thursday, after Jessica Pegula beat 2021 US Open champion Emma Raducanu 6-4 6-7 (7-3) 6-2 in a two-hour, 25 minute battle finishing at 11.23pm (local time).
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