At the Zhuhai Championships two days later he got that landmark first victory.
He lost his next match, to eventual champion Alex de Minaur, and said afterwards that he was playing “top 70, top 60” tennis.
Most observers felt that the three-time Grand Slam winner, who only returned to playing singles in mid-August, was being harsh on himself.
Last week he moved on to the China Open in Beijing, which boasted a stronger field, and offered more proof that his comeback was moving along very nicely.
In his opener Murray claimed his biggest post-surgery scalp yet, defeating 13th-ranked US Open semi-finalist Matteo Berrettini.
Murray has consistently said his hip is pain-free but that he does not have the fitness to play several matches a week and needs to be quicker across the court.
Nevertheless, the next day he beat fellow Briton Cameron Norrie in three sets.
Victory brought another small landmark, putting Murray in the quarter-finals of a tournament for the first time in a year.
He lost in the last eight to top seed Dominic Thiem, who would go on to win the China Open, but said afterwards that the comeback was going better than expected.
“I think this (week) was maybe the best in terms of how I played since I came back,” Murray said.
His ranking, which had plunged to 503, jumped to 289.
‘I can do much better’
Murray stepped up his return at the Shanghai Masters this week, defeating 56th-ranked Argentine Juan Ignacio Londero in three sets in his opener on Monday.
On Tuesday he faced his toughest opponent yet, the 12th-ranked Fabio Fognini.
Murray twice served for the match but eventually went down in three sets, after which he accused the Italian of trying to put him off by shouting while he went for a volley.
It was a bitter end to a day which began with the Australian Open announcing that Murray will return to Grand Slam tennis there in January.
It will be a fitting return because it was in Melbourne nine months ago that Murray broke down in tears and said that his career could be over because of his troublesome hip.
There were high emotions again after defeat to Fognini, but this time anger — with himself for failing to close out the match, and with his opponent’s histrionics.
“There is a lot of things that I need to get better at and I can do much better,” a fuming Murray said.
“I will go away and I’ll work on those things and be in a better position next time I play against him.”
Murray told AFP in Zhuhai that success in China would be winning two matches at each of the three tournaments.
He did not manage that, but on this evidence, coupled with his deserved reputation as a fighter, few would bet against Murray capping his comeback with a 46th title.
Next he will play at the European Open in Antwerp, which starts on Monday.