The 19-year-old produced a stunning nine-under-par 63 to overturn a seven-shot deficit and finish the regulation 72 holes tied with overnight leader Ben James at 23 under par.
Brown, who skipped college to turn professional straight out of high school, carded 10 birdies in the lowest round of the day at Cabo San Lucas.
He held his nerve to sink a six-foot birdie putt on the 18th hole and take the clubhouse lead, but James responded with an eagle on the same hole to force a sudden-death playoff.
Both players reached the green in two during the first playoff hole but narrowly missed their birdie attempts.
They returned to the 18th tee, where both approaches again left them with challenging putts. James pushed his six-foot effort wide after a fine chip, allowing Brown to sink his putt and secure a remarkable victory.
"Playoff holes are just... they're incredible. It tests you in so many different ways," said Brown, who had a lengthy wait between the end of his round and the playoff.
"I was hitting balls and saw he made it, and I was like, 'All right, playoff, let's go.'
"I've known Ben since we were amateur golfers, and he's just such an unbelievable player. He's lights-out with the putter.
"I got him this time, but I'm sure we're going to be battling out years to come."
At 19 years and five months, Brown is the fourth-youngest PGA Tour winner in history, surpassing Jordan Spieth's victory at the 2013 John Deere Classic at 19 years and 11 months as the youngest in modern times.
Michael Kim finished third, one stroke back at 22-under-par, having birdied the final hole moments before his Sunday playing partner Brown followed suit to retake the lead.
Japan's Kensei Hirata was fourth at 21-under, with David Ford fifth a further stroke back.
Brown had already attracted attention earlier this year when he carded a 12-under-par 60 at La Quinta, sharing the halfway lead with world number one Scottie Scheffler, who went on to win the tournament.
He also claimed an impressive third-place finish at the Puerto Rico Open.
"It's crazy... to finally get my first one under my ball is pretty special," said Brown.
Ben James fired a 6-under 66 to stretch his lead to four shots at 21-under after the third round of the 2026 World Wide Technology Championship at the Tiger Woods-designed El Cardonal at Diamante in Los Cabos, Mexico on Saturday.
Ben James surged into a one-shot lead at the World Wide Technology Championship after firing an eight-under-par 64 in Friday's second round.
Chris Kirk grabbed the lead at the World Wide Technology Championship on Thursday, carding a nine-under-par 63 to take a one-shot lead after the opening round.
Jon Rahm is charting his way back to the PGA Tour after negotiating his exit from LIV Golf, and he's prepared to pay the price.
