The ninth seed looked in control for two sets against his opponent but Fils, bidding to become the youngest Frenchman in the professional era to reach a Grand Slam quarter-final, responded superbly to extend the Court One contest.
De Minaur, watched by his girlfriend Katie Boulter, the British number one, moved clear in the fourth set though to nip the Fils' comeback in the bud.
Worryingly for the Aussie, who will play seven-time champion Novak Djokovic in the quarter-finals, he appeared to be in some discomfort at the end.
"I'll be alright," De Minaur said on court when asked if he had sustained an injury. "I made it harder than I should have and happy to get over the finish line."
Talking to reporters later he said he had felt a "bit ginger" and said the problem was his hip.
"Just slid out to a forehand on my first match point. Felt like I jarred it a little bit. Kind of was a little bit ginger. Again, it's probably a little bit of a scare more than anything," he said.
"I'm feeling pretty decent. Again, body went through a pretty physical match out there. Body feels a little bit ginger everywhere. I'm not going to lie.
"I've done my recovery. I'm sure I'll be feeling great tomorrow."
De Minaur has previously reached two Grand Slam quarter-finals, losing to Dominic Thiem at the 2020 US Open and Alexander Zverev at the French Open this year.
With no British players left in the singles draws after Emma Raducanu's defeat on Sunday, De Minaur said being Boulter's partner qualified him for home support.
"I'll take all the support I can get. I can be the honorary Brit here at Wimbledon," he joked.
"Definitely over the years I've learnt a lot more about the British culture thanks to Katie. I'm getting there."