Matsuyama began the day with a five shot lead and was two-under for his round until he got into trouble with bogeys on the 12th and 14th and then a double bogey on the par-4 15th.
That allowed Xander Schauffele, who had started the day nine shots off the lead, and Norway's Viktor Hovland to join in him in a three-way share of the lead on 15-under.
But with a possible three-way playoff or even worse looming for Matsuyama, he rediscovered his touch in the nick of time.
He sank a 26-foot birdie putt on the par-4 17th to regain the lead and, with his rivals already in the clubhouse, needed just a par on the 18th to clinch the first of the three events that make up the FedEx Cup playoffs.
There was no sign of nerves, however, as he attacked the par-4 final hole, making birdie to end on 17-under with Schauffele and Hovland tied second.
"After the 14th hole, I was still two up, but I knew Viktor and Xander were playing 15, 16 ahead of me. I figured they would both get to 16-under. So when I was playing the 16th hole and looked at the scoreboard, sure enough, they were both at 16-under and I was a stroke back," said Matsuyama.
"I felt today's victory slipping away at that point because 17 and 18 are difficult holes enough, let alone to birdie them.
"But I was fortunate enough to birdie 17. Immediately I thought, oh, man, this is going to be a tough tee shot at 18. I've got to keep it in the fairway. I'm grateful I was able to do it," he said.
The win was the 10th on the PGA Tour for Matsuyama, the 2021 Masters winner, and his second this season following his victory at the Genesis Invitational in California in February.
Matsuyama had to play this week with a stand-in caddie after his regular bag carrier had his passport stolen in London in a theft which also saw the golfer's wallet stolen.
Schauffele, who triumphed in the PGA Championship and the British Open this year, was bogey free for his seven-under round of 63.
Hovland, who shot 66, got himself in real contention with birdies on the 15th and 16th but then made bogey on the 17th.
The playoff field will be cut to 50 for next week's BMW Championship at Castle Rock, Colorado and then slimmed down further to 30 for the final event, the Tour Championship in Atlanta starting on August 29.
Scottie Scheffler is the current leader of the playoff standings with Schauffele second and Matsuyama projected to move up to third with this win.
Nick Dunlap, the 20-year-old American who turned professional in January afer winning The American Express tournament in California, pushed himself into the top-50 after finishing tied for fifth.
