Norrie had two match points in a marathon third-set tie-break but lost 7-6 (6) 3-6 7-6 (9) in two hours and 15 minutes.
Australia's Jordan Thompson caused an early upset at the Queen's Club tournament in London with a first-round win over seventh-seed Holger Rune on Monday.Thompson came from a set down to defeat Rune, a semi-finalist at the grass-court warm-up event for Wimbledon last year, 4-6, 7-6 (7/4), 6-3 in a match lasting more than two hours.
Draper powered his way to an impressive first ATP Tour title in Stuttgart last week.