Draper won the prestigious Masters 1,000 title at Indian Wells and reached the fourth round of the Australian and French Opens in a promising start to his 2025 season.
But he began struggling with a bruised bone in his service arm during the clay-court swing in April, and the issue progressively worsened.
Determined to complete a full recovery from the issue, Draper took the decision to miss the Australian Open in January before making his return for Great Britain on 5 February.
Seeded fourth in Dubai, Draper had to withstand a set point when serving at 5-4 down in the opening set but went on to edge a tight tie-break by winning three consecutive points to overcome an 8-7 deficit.
Despite first-set opportunities for both players, the first break of serve in the contest did not arrive until the fourth game of the second set when the 68th-ranked Halys hit wide to give Draper a 3-1 lead.
Draper served out victory untroubled from there, conceding just two further points on serve as he ending the match with an impressive 86% win rate on his first serve.
The left-hander’s successful recovery from injury was also underlined by the fact 19 of his 24 winners flew off his previously affected forehand side.
Meanwhile, it was a mixed bag for Britons Katie Boulter and Cameron Norrie in Mexico.
Boulter, 29, came through her first-round tie with Beatriz Haddad Maia 6-4 6-4 at the Merida Open in Mexico.
But seventh seed Norrie, 30, fell to a surprise 6-3 6-2 defeat by Spain’s Rafael Jodar at the Mexican Open.