Matsuyama made three bogeys in his final four holes but a closing one-over 73 was good enough for a one-shot victory at Augusta National.
The 29-year-old Matsuyama finished at 10-under 278 with tournament rookie Will Zalatoris second after a two-under 70.
Jordan Spieth (70) sealed his fifth top-five at Augusta with a share of third alongside Xander Schauffele (72) at seven under.
A charge from Marc Leishman never materialised, with the Australian signing for a 73 to tie for fifth at six under, with Jon Rahm, whose 66 was the best round of the final day.
Matsuyama's four-shot overnight buffer was slashed briefly to just one after a nervous opening-hole bogey but after a birdie on the second he took control.
Only Zalatoris and Matsuyama's playing partner Schauffele were providing anything close to a threat to a monumental victory.
Matsuyama, who first made his debut at the Masters by finishing low amateur as a teenager a decade ago, played excellent yet conservative golf around the potentially deadly Amen Corner after making the turn with a five-shot buffer.
But things got interesting when Schauffele tapped in for his third straight birdie at No.14 to close the gap to four.
Matsuyama fired his second shot at the par-5 15th over the green and into a pond on his way to a bogey while Schauffele got up and down from the greenside bunker for birdie to cut the deficit in half.
But Schauffele's hopes were sunk when his tee shot at the 16th found water and he made the first triple-bogey of his major championship career.
Matsuyama made bogey at the par-3 to be three shots clear of Zalatoris, who salvaged a par at the final hole after driving in the bunker to be in the clubhouse at nine under.
Despite a bogey on the 18th, Matsuyama claimed his first win in four years to cement superstar status in his home country.
It was not the round Leishman wanted despite going within a whisker of making an ace on the 16th hole.
Cameron Smith, last year's joint runner-up, was the next best Australian with a 70 giving him a share of 10th at three under.
Matt Jones had a 72 to end his Masters at one over while 2013 champion Adam Scott signed off with a 73 to finish the week 11 over.