'This winning thing isn't that easy,' admitted Herron, who pocketed $1,080,000 for the win.
At the first playoff hole, the par-4 18th at Colonial Country Club, Johnson found the fairway off the tee, then Herron hammered his drive nearly 50 yards past Johnson.
Neither player hit a good approach as Johnson's ball rolled 40 feet right of the stick. Herron's second from 78 yards came up 50 feet short of the target and both golfers lagged their putts to tap-in range for par.
The next extra hole was the par-4 17th and Johnson's drive bounced into the first cut on the left side. Herron thumped another long drive, which was a nice change from regulation where his tee ball came to rest in thick rough on the right side.
Herron was first with his approach and knocked his shot to 8 feet. Johnson's second checked up short of the flagstick about 25 feet from the hole.
Johnson missed his par try and tapped in for par. Herron, affectionately nicknamed 'Lumpy,' converted his birdie opportunity and pumped his fists in the air.
'I'm going to be on that wall with Mr. Hogan and Crenshaw and a lot of great names,' said Herron, referring to a wall at Colonial that has every past champion etched on it. 'That's special. No one can take that away from me.'
Rod Pampling, who shared the overnight lead with Herron, was tied for first with Herron until a disastrous double-bogey from under a hedge at 15. He finished with an even-par 70 and came in third place at 10-under-par 270.
Johnson flew out of the gate on Sunday with a two-putt birdie at the first, then a 7-foot birdie putt at the second. He parred every hole on the front nine until a three-putt bogey at the ninth.
The Swede trailed by as many as three even after two birdies and a bogey on his first four holes of the back nine. When Herron and Pampling came back to the pack with inconsistent play on the second side and Johnson was ready to pounce.
He three-putted the 16th green for a bogey, but still had life. He ran home a long birdie putt at the 17th, then hit his approach to 6 feet to set up birdie at the last.
'When I three-putted 16 I thought I was out of it,' admitted Johnson. 'I had no idea what was going on behind me. My caddie said to me on 17, 'just hit it in the middle of the green.' I thought if we could squeeze one more out, at least I could have a good chance at second.
'I'm very pleased. Very, very pleased.'
Herron traveled a different route to the playoff. He collected three birdies in his first four holes to climb to the top of the leaderboard, but pars the rest of the way on the opening side brought others back into the tournament.
Herron was tied with Pampling after Herron missed a 7-foot par putt at the 10th. Both Herron and Pampling birdied 11, but Herron moved back into the lead with a 12-foot birdie putt at the 12th, a hole where Pampling missed a 4-footer to keep pace with Herron.
Pampling drew even when Herron three-putted the 14th green for a bogey. At the next hole, Pampling missed the fairway then sent his approach right under a hedge near a cart path. He got much more of the ball than he thought he could because his chip ran through the putting surface. Pampling chipped to 8 feet, but missed that try to fall out of contention.
Herron dropped another shot at the par-3 16th when he could not save par from the lip of a bunker. Johnson made the move up the leaderboard, so the pressure was back on Herron's shoulders.
At the 17th, Herron drove into the right rough, then missed the green left. He chipped to 12 feet and sank the par putt to remain tied with Johnson, who was in the clubhouse.
One hole later, Herron's tee ball skipped into the right rough near trees. His approach came up short and left, then Herron chipped to nine feet. Herron drained that par putt and moved on to the winner's circle two playoff holes later.
Players Championship winner Stephen Ames (63), Ben Crane (64), Brett Quigley (66), Stewart Cink (68), Peter Lonard (70), Nathan Green (70) and Pebble Beach winner Arron Oberholser (67) tied for fourth place at 9-under-par 271.
Defending champion Kenny Perry struggled to a 1-over 71 and tied for 37th place at minus-3.