Matsuyama displayed supreme poise in the clutch, overcoming a late two-stroke deficit in regulation as he finished birdie-birdie to catch Fowler at the TPC Scottsdale.
He then edged the American at the fourth extra hole to claim his second PGA Tour victory, following his maiden success at the Memorial tournament in 2014.
"It's been a while since the first one and I'm just really happy today," Matsuyama told Golf Channel via an interpreter.
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"At the start of this week I wasn't really playing that well. Winning wasn't one of my thoughts. I'm just glad everything worked out fine."
Shigeki Maruyama, with three wins, is the only Japanese player with more victories on the PGA Tour.
Matsuyama, 23, who has also won six times on the Japan Tour, is projected to rise to 12th in the world rankings.
A Matsuyama victory seemed most unlikely when Fowler stood over an eight-foot birdie chance at the par-three 16th stadium hole with a chance to go three shots ahead.
But Fowler missed the putt, much to the disappointment of the gallery, and then compounded his situation by powering a driver into the water beyond the 17th green en route to a bogey.
In a dramatic finish to regulation, Matsuyama rolled in a 15-foot birdie dead centre at the par-four 18th, before Fowler matched him by sneaking a nine-footer in the right-hand door.
They both shot 67 to finish at 14-under-par 270, two strokes ahead of American Harris English.
New Zealand's Danny Lee, who started the day with a three-shot lead, stumbled early and shot 73 to finish fourth, three shots off the pace.
Matsuyama and Fowler opened the sudden-death playoff by playing the 18th twice, matching each other first with par and then birdie, before continuing at the par-four 10th, which they both parred.
The playoff finally ended at the par-four 17th, where Fowler drove into the hazard for the second time in barely an hour and could not save par.
Matsuyama had the luxury of two-putting from five feet to win, as world number four Fowler squandered a chance for his second victory in three starts, after winning the European tour's Abu Dhabi Championship two weeks ago.
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