Johnson carded a six-under-par 65 to finish 20 under overall alongside Matteson, who had led since day one but could only manage a two-under 69, his worst round of the week, on the final day.
That took them to a play-off hole on the 18th which, remarkably given the week's low scoring, both players contrived to double bogey.
They played the hole again, and this time Johnson birdied, while Matteson could only manage a par four.
The win takes Johnson fifth in the American Ryder Cup standings, while Matteson, 368th in the world, has the consolation of taking the final exempt spot in The Open.
Johnson's play-off birdie came thanks to an exquisite 192-yard approach shot, from the same bunker he found in the first play-off hole, which was within inches of giving him an eagle.
"I think we're stating the obvious," he told www.pgatour.com. "That was really good. That was my shot of the week."
As Johnson, who as an Iowan and strong supporter of the tournament had support from the Illinois crowd, made steady progress, carding two birdies in his front nine and four on the back, Matteson appeared to have let his chance go with a double bogey at 15.
That left him level for the day, but an eagle three at the 17th took him into a play-off.
"All in all, you go into a play-off and lose to a shot like that, I mean, that's an unbelievable shot," said Matteson. "To hit it six inches to that hole location, I mean, if you ask most pros, they'll take middle of the green where my ball was all day long.
"My hat's off to Zach. He drove it in the bunker twice and figured out a way to win. It's a great story, you know, hometown kid. It was really good."
At the start of the day, much of the talk had been about Matteson's playing partner, Steve Stricker, who was going for his fourth straight John Deere title.
Stricker started the day in second, three shots behind Matteson as he looked to equal the feat achieved by Young Tom Morris at Prestwick in 1968-72 and also by Walter Hagen at the USPGA Championship, Gene Sarazen in the Miami Open and Woods at both Bay Hill and the Buick Invitational.
At two under through three and three under through 11 he was well in the mix, but it all fell apart over the last four holes, where three bogeys ruined his chances.
He finished one under for his final round and 16 under overall for a share of fifth alongside Luke Guthrie, who carded a best-of-the-day seven-under 64.
"Maybe I was trying too hard," said Stricker "I don't know. I don't know really what it was. I was trying to win the golf tournament. I wasn't worried about four in a row, I was just trying to win."
He added: "It's been a little bit of a tiring week. You know, a lot of expectations, a lot of things going on here - all good things, don't get me wrong - but it takes a lot out of you, too.
"Although I wish I could have been out there in a play-off or tried to have won again, yeah, I'm kind of glad it's over.
"Hopefully I'll come back next year and start another one."
Scott Piercy was third on 18 under and Australia's John Senden fourth on 17 under.
England's Gary Christian had a disappointing final round as a level-par 71 saw him finish in a share of 19th on 12 under.