British number three Jacob Fearnley, 23, also went out after a crushing straight-set defeat by top seed Alexander Zverev.
The German, who also beat the Scot in straight sets at the Australian Open, needed just one hour, 14 minutes to wrap up a 6-2 6-4 victory.
Despite the defeat, Fearnley will climb above Cameron Norrie to become British number two – behind Draper – when the ATP rankings are updated after Miami.
Elsewhere, 20-year-old Coleman Wong of Hong Kong secured the first top-20 win of his career with a 7-6 (7-3) 2-6 7-6 (7-5) victory over American world number 14 Ben Shelton.
American third seed Taylor Fritz eased through to the next round with a 7-6 (7-2) 6-3 win over beat Lorenzo Sonego of Italy.
BBC News
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