Murray faced American Sandgren in the second singles match of his comeback last month, losing in two close sets, and this was a demonstration of the progress he has made since then as he claimed a 6-3 6-7 (6) 6-1 victory.
Not since a first-round win over James Duckworth in Brisbane right at the start of the season, prior to the hip resurfacing operation he underwent at the end of January, had the former world number one won a contest at this level.
— ATP Tour (@ATP_Tour) September 24, 2019
Murray played his first tournament at second-tier Challenger level in 14 years in Majorca while his rivals were doing battle at the US Open and had been training hard since ahead of four consecutive tournament weeks.
And the improvements were clear, with Murray moving by far the best he has in any of his singles matches so far and serving strongly.
Those two things enabled him to be more attacking in his play, and it was particularly encouraging how much weight he was managing to get behind his forehand.
There were also classic Murray touches – a deep defensive lob from a seemingly impossible position to win one point in the second set, and a handful of flicked winners after chasing down drop shots.
— LTA (@the_LTA) September 24, 2019
Murray, who did not face a break point during the match, took the first set with a break of serve in the sixth game and had a match point at 6-5 in the second-set tie-break.
But Sandgren, ranked 69, saved it and made it three points in a row to take the contest to a third set.
In humid conditions, this was a test of Murray's physical condition but it was Sandgren who was found wanting.
After Murray broke to lead 3-0, the American took a long medical time-out to have strapping applied to his foot and then dropped serve again after a mammoth game.
Murray was unable to take two chances to finish the match with a bagel set but polished things off in his next service game and will take on Australia's Alex De Minaur in the second round.