The 23-year-old, the number third-time player Jacob Fernley, was strayed after a direct and direct defeat by Alexander Zverev was extinguished.
The German, who also beat the Scotland in the Australian Open live in a direct set of the Australian Open, needed to win 6-2 6-4
Despite the defeat, Fernley climbs Cameron Nori to become British – after Draper – when the ATP rankings are renewed after Miami.
Elsewhere, Coleman Woong, 20, won his first 20 best career at Hong Kong by winning 7-6 (7-3) 2-6 7-6 (7-5) in the United States number
Taylor Fritz finished third in the next round of the next round, 7-6 (7-2) beating Lorenzo Sonego 6-3