Brown became the youngest winner since Charles Kocsis won the Michigan Open in 1931 as an 18-year-old.
James lost a four-shot lead going into the final round at El Cardonal at Diamante on Sunday (Monday AEDT), then showed his moxie by smoking a 285-yard shot into 20 feet on the par-5 18th and making eagle to salvage a 70 and force the playoff.
But he missed an eight-foot putt on the second playoff hole, and Brown made his three-footer.
"I'm so obsessed with this game. It tests you in so many ways," said Brown, who graduated high school in January.
"I love golf, all the stuff that goes into it and I can't wait for what's next."
For a sleepy FedEx Cup Fall event on the southern tip of Baja California, this was pure theatre between two players from the next generation.
James was the No.1 player in the PGA Tour University ranking last season. Brown made a surprising choice to turn pro two years ago while a junior in high school.
Brown was tested even more by going through two bags of golf balls on the range waiting to see if the two-shot lead he had over James would hold, then going back out to the 18th to decide it.
On the first extra hole, their approach shots were virtually side-by-side, and both narrowly missed eagle chances. They returned to the 18th tee and their drives were again next to each other, and both came up just short of the green.
James nearly holed his pitch and saw it run out eight feet. Brown, who had a similar pitch in regulation that he hit to six feet for a closing birdie, this time came up three feet short. James' birdie putt grazed the right edge, and Brown poured in the winner.
The pair have known each since their junior days and Brown figures this is just the start.
"I got him this time, but I'm sure we'll be battling it out for years to come," he said.
With eight players separated by two shots on the back nine, Brown ran off three straight birdies to share the lead, then left the mistakes to everyone else.
Brown hit a superb pitch for birdie on the final hole to post at 23-under 265.
That put him one shot ahead of Michael Kim, who played with the Tennessee teen and made birdie from 12 feet for 64 right before Brown made his putt.
Brown earned his PGA Tour card for 2027 by finishing among the top 20 on the Korn Ferry Tour points list. Now he has a two-year exemption, which puts him in the elite Championship Series when the PGA Tour's new model begins in 2028.
The victory also assures Brown of his first major next year at the PGA Championship.
It was another setback for James, who in 13 starts since turning pro has five top-five results, and two runner-up finishes.
The only Australian to make the cut, Cameron Davis, finished tied for 42nd at 12 under after a disappointing one-over 73 in the final round.
