The 24-year-old from Perth moved to 98th in the ongoing live rankings as he claimed his biggest career victory by knocking out the ATP NextGen champion from last November.
Schoolkate, son of a tennis coach, won his first match over a top-50 opponent on his sixth attempt as he dealt out the number 49 teenager from Brazil. The qualifier played a quarter-final this month in Los Cabos and won through qualifying for his spot in the Masters main draw.
"I'm very happy with the result," Schoolkate said. "I played a good match and made it tricky throughout.
"He's so young (18) but already an established player. I'm looking forward to my next match."
Schoolkate advanced with 10 aces among his 23 winners.
He caught Fonseca in a first-set tiebreaker and broke for a 2-1 lead in the second set on his way to victory in windy and quick court conditions.
"The conditions suit the way I play," he said. "I like to serve big and get forward to make things uncomfortable for the opponent."
The Aussie said he had given some thought to his potential top-100 breakthrough but is not stressing over any self-imposed deadlines.
"My goal now is to be in the top 100 but I'll just keep playing week-in, week-out, pushing hard and it will come," he said.
World number three Alexander Zverev is the top seed of the expanded 12-day event, which will play its final on a Thursday instead of the more traditional Sunday.
ATP number one Jannik Sinner and second-ranked Carlos Alcaraz along with Novak Djokovic all withdrew with various injuries and fatigue issues prior to the tournament, which began only a fortnight after the Wimbledon final.