Czech teen Mensik into first Masters semi-final in Miami
Fils had enjoyed one of the biggest wins of his career on Wednesday when he defeated top-seed Alexander Zverev but he struggled to repeat the feat against the impressive 19-year-old Mensik.
The towering Czech's big serve was too much for Fils, who had come through three-set battles with Frances Tiafoe and Zverev and showed signs of tiredness.
"It feels incredible. I think the biggest result so far in my career, so I'm glad I just kept going since the first round," said Mensik.
"That's the key, to keep the focus during the two weeks, because it's always tough. The job is not done."
Mensik broke out to an early 4-1 lead but then let Fils back into the contest with the 20-year-old Frenchman forcing a tie-break.
But having survived that comeback from Fils, Mensik was rock solid in the second set as he powered his way to victory in 75 minutes.
Mensik, ranked 54 in the world, will next face the winner of the quarter-final between Taylor Fritz and Matteo Berrettini later on Thursday.
In the remaining quarter-final, postponed from Wednesday, fourth-seed Novak Djokovic takes on American Sebastian Korda with the winner up against Bulgarian Grigor Dimitrov.