Wilson, the former Northwestern player who missed the cut in 11 of his previous 13 tour starts this year, birdied the final hole of regulation for a 5-under 67 to match Harrington, also a former Northwestern player, at 21-under 267.
"It's comforting knowing I can perform when it matters most," Wilson said. "Anyone can do it in practice."
Harrington shot a 68, also birdieing the final hole of regulation at Highland Springs, but hit his second shot into the water on the par-5 closing hole in the playoff.
"I've known Chris a while and we're good friends," Harrington said. "If I could be in a playoff with anybody in this field, it would be him."
Wilson made $112,500 after entering the week with only $6,486 in earnings. He jumped from 165th to 23rd on the money list, with the final top 25 earning 2013 PGA Tour cards.
"I've been close the past couple weeks," Wilson said. "When you have confidence in your putter it just frees up every other aspect of your game."
He recently met with sports psychologist Bob Rotella in Virginia.
"We simplified a lot of things," Wilson said. "We changed my approach to putting and that's helped to eliminate a lot of the distractions I was having."
Andy Winings shot a 65 to finish third at 20 under.
Ben Kohles, the winner of the previous two events in his first two starts as a professional, tied for 60th at 8 under.