The Australian 10th seed recovered from a break down in the deciding set to triumph 5-7 7-5 6-3 in two hours 33 minutes, in what was the first meeting between the pair.
De Minaur had not won three matches in succession at any event since reaching last month's Rotterdam final, where he fell in three sets to four-time grand slam champion Carlos Alcaraz.
World No.60 Fonseca, 18, is an unbelievable 27-5 in his last 32 matches - which includes four titles - but it's the Demon who will next face 29th-seeded Italian Matteo Berrettini.
"It was a hell of a battle," de Minaur said after digging deep to post a tour equal-best 17th win of the season.
"I knew coming in what to expect. Not only is he an incredibly talented, dangerous, explosive player, but he's playing with so much confidence at the moment."
De Minaur's less-heralded compatriot Adam Walton earlier celebrated also securing his last-16 place at the Masters 1000 event.
"I shouldn't even be here," admitted the stunned qualifying 'lucky loser' after beating wildcard Coleman Wong 7-6 (8-6) 4-6 6-4 to set up a duel with American third seed Taylor Fritz, in what will be the biggest match of his life.
The 26-year-old Queenslander had been knocked out in qualifying last Tuesday by compatriot Tristan Schoolkate, but hung around hoping to snag a place as should any of the qualified players drop out.
Fourth on the list to get that coveted second chance, it seemed unlikely he would get a late place.
Walton was about to buy a ticket on Saturday to fly to Mexico to take part in a second-string Challenger event when the call came that the No.21 seed Hubert Hurkacz had pulled out with injury, and that he would replace him.
If that wasn't lucky enough, the even more fortunate news for Walton was that Hurkacz had a bye, so the Aussie was guaranteed a place in the second round.
In that match on Saturday, Walton beat Italian Luciano Darderi, setting him up for Monday's clash against Wong, who was just as amazed to be in the third round after knocking out American star Ben Shelton in the previous round.
But with both men battling to reach rarefied heights - world No.182 Wong is the first man from Hong Kong ever to win a match at this level - it was Walton who prevailed in a dogfight over two hours 18 minutes on court one at the Hard Rock Stadium.
"I'm very happy right now, it's just very good fortune this week," Walton said after posting only his sixth tour-level victory.
"I got thrashed in qualifying and got the call three days later to play again, it almost feels like a new start, a new tournament.
"Wins have been hard for me on the Tour. I've done well at the Challenger level but playing these big tournaments is obviously very rewarding, especially if you can win matches, because they offer the biggest prize money."
So while Walton could celebrate his $US60,000 ($A95,000) pay day, there was only predictable disappointment for Australian No.3 Jordan Thompson, who couldn't capitalise on a fast start and succumbed 7-5 6-4 to top seed Alexander Zverev of Germany.
The Sydneysider raced into a 4-1 lead but Zverev reeled him back in, winning five games on the trot to take the first set and control of the second, before running out a winner in 90 minutes.
