The former world No.1 underwent hip surgery after losing in the first round of the Australian Open in January, and though there were fears for his future in tennis, he made a doubles comeback earlier this year.
After that was deemed a success, he played singles in Cincinnati and Winston-Salem in August but skipped the US Open to work on his fitness, choosing to play at challenger level in Mallorca, where he won his first two matches.
He was drawn against Tennys Sandgren, a former Australian Open quarter-finalist in the first round, who defeated him in straight sets in Winston-Salem and won the first set convincingly, breaking in the sixth game of the match and never looking back.
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Murray continued to probe in the early exchanges of the second set, using his drop shot effectively but was forced into a tiebreak, where he missed a match point and when the American rattled off three straight points, the encounter was going the distance.
The Scot had no issues with his movement throughout the match and showed no signs of wilting when he moved into a 4-0 lead in the decider, the second break coming in an epic 19-minute game.
Sandgren saved two further match points but Murray served it out to record a win that will mean a great deal to him.
Murray faces seventh seed Alex de Minaur next.
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