Matsuyama birdied the hole in regulation and two-putted for par from 6 feet in the playoff.
Fowler forced the playoff with a 10-foot birdie putt on the par-4 18th after Matsuyama made an 18-footer.
They each shot 4-under 67 to finish at 14-under 270.
The playoff was just as dramatic in front of another big crowd at TPC Scottsdale's Stadium Course on a sunny day with the temperature in the high 70s.
On the par-4 10th on the third extra hole, Fowler saved par with a 12-foot putt after driving into the left rough and skulling his approach long and right.
Matsuyama made a 5-footer to extend the playoff.
They played the 18th hole twice to open overtime.
On the first extra hole, Fowler chipped to a foot to set up a par after leaving his wedge approach short and right.
Matsuyama rolled his 25-foot putt inside a foot.
On the second playoff hole, Matsuyama matched Fowler's 15-foot birdie putt to extend it.
Matsuyama won the 2014 Memorial for his only other PGA Tour title, beating Kevin Na on the first extra hole.
The 23-year-old Japanese player tied for second last year in Scottsdale, a stroke behind Brooks Koepka.
Fowler missed a chance for his fifth worldwide win in nine months.
He started the run in May at The Players Championship, won the Scottish Open the week before the British Open, the Deutsche Bank Championship in September and the European Tour event two weeks ago in Abu Dhabi.
Fowler chipped in from 50 feet for birdie on the par-4 10th to take the lead and added birdies on the par-5 13th and 15th holes to pull two shots ahead.
He missed a 10-foot birdie putt on the par-3 16th, the tournament's signature stadium hole, before giving Matsuyama a chance with the aggressive tee shot on 17 that went nearly 360 yards.
The crowd of 65,330 yesterday pushed the week total to a record 618,365, shattering the mark of 564,368 set last year.
The event broke its own golf record on Sunday at 201,003 after drawing a Saturday-record 160,415.
Harris English shot a 66 to tie for third at 12 under.
Phil Mickelson followed his third-round 65 with a 71 to tie for 11th at 8 under.
The 45-year-old won the event in 1996, 2005 and 2013.