Draper secured a comfortable 6-2 6-2 victory over Norway’s Viktor Durasovic in the Davis Cup in Oslo.
His recovery from a complex 'bone bruising' injury in his left arm led him to miss the Australian Open and intentionally step back from watching tennis.
Cameron Norrie also contributed to Great Britain's lead, winning his match 6-4 6-4 against Nicolai Budkov Kjaer.
Great Britain now holds a 2-0 lead against Norway in the Davis Cup qualifying round, with the opportunity to secure the tie in Friday's doubles match.
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