Share the Upside made his first start on the grass a memorable one, when he won a five-eighths of a mile allowance in a swift 55.64 seconds.
Share the Upside pressed Lawton through an opening quarter in 21.67 seconds and a half-mile in 43.89 before edging past that one.
Stewart Elliott was aboard the winner, his fourth on the day at Lone Star. Of his wins, three came for Share the Upside's trainer, Steve Asmussen.
Share the Upside paid $5.20.