Woodland trailed second-round leader Andres Romero by two points coming into Saturday's play, but used a chip-in for an eagle on the par-5 second hole to grab the advantage.
Woodland, seeking his second career PGA Tour win and first since 2011, has racked up a total of 37 points through three rounds at Montreux Golf & Country Club.
Brendan Steele forged into sole possession of second place at 30 points with 17 points Saturday.
David Mathis tallied 12 points to corral third place with 29 points, while Romero stumbled to just five points Saturday, dropping into fourth place with 27 total points.
Holding sixth place at 25 points was Charlie Wi (six points).