Tway birdied seven straight holes beginning at the sixth. Slocum made nine birdies with no bogeys.
Australian Aaron Baddeley was alone in third at 8-under 62, having put together his round early in the day.
Sergio Garcia marked his return to the PGA Tour with a 2-under 68 and attracted the largest gallery of the day.
Tway is coming off a two-week rest after winning at the Bell Canadian Open earlier this month.