Matteson, who led wire-to-wire during the four-day event, forced a playoff despite double-bogeying the 15th hole -- he drained a 60-foot eagle putt on the par-five 17th to make up the strokes.
Matteson finished with a round of 2-under-par 69 while Johnson charged from behind to fire a 6-under 65, forging a 72-hole tie at 20-under 264.
Both golfers hit the water hazard on the first playoff hole, ending with identical double-bogeys, but Johnson grabbed the advantage on the second hole when his 193-yard second shot rolled to within a foot of the pin.
Matteson couldn't drain a long birdie try and Johnson tapped in for the victory.
Three-time defending champion Steve Stricker ended up in a tie for fifth place at minus-16. Stricker was attempting to become the fifth golfer in history to win the same tournament in four consecutive years.