Schenk made a 25-foot putt on the par-4 18th for his first tour victory after closing with a bogey on the last hole in regulation to fall into the playoff.
"What an unbelievable experience," Schenk said. "I can't believe I'm holding [the trophy]. I thought I lost the tournament two or three times and was just lucky to make that last putt."
The 25-year-old former Purdue player shot a 1-over 72 to match Axley (66), Kropp (67) and third-round leader Thompson (74) at 14-under 270 at Panther Creek.
Schenk earned $99,000 to jump from 42nd to 11th on the money list, with $156,741. The top 25 at the end of the regular season will earn PGA Tour cards.
Thompson shot 64-64 to take a two-stroke lead over Schenk and Whitney into the final round.