0454 GMT November 19, 2019
The Briton defeated US Open semifinalist Matteo Berrettini 7-6 (7/2), 7-6 (9/7) in just over two hours at the China Open in smoggy Beijing, AFP reported.
Murray meets compatriot Cameron Norrie in the last 16 after a gutsy victory over the 13th-ranked Italian.
Murray, 32, a three-time Grand Slam winner, said he had made big strides since the first singles match of his return, a defeat at the Cincinnati Masters in mid-August.
Last week in Zhuhai he won his first ATP singles match since January's major operation.
"I didn't really feel like I was playing at a great level," he said of his match against Richard Gasquet in Cincinnati.
"Whereas even last week (in Zhuhai), although I lost in the second round, I felt like I was playing tour-level tennis."
"I think things are going in the right direction," added Murray.
Now ranked 503 in the world, he fought back from a break down to force a tiebreak in the first set against the Italian Berrettini.
Murray showed glimpses of the steely determination which made him number one in 2016 as he grabbed the first set from the eighth seed.
The second set went with serve and again to a tiebreak, with Murray saving two set points on the way to a win.
Murray said that patience was now the key.
"Last week was a big step for me," he said.
"Now I just need to try and get the matches, get them consistently, so that I'm used to playing three, four matches in a week.
"Right now, at this level, I don't know if I'm ready to do that or not.
"So the more I can get through these sort of matches like I did today, I'll get there a little bit quicker."
Trio into last 16
On the women's side of the tournament, world number one Ashleigh Barty, reigning champion Caroline Wozniacki and Naomi Osaka all comfortably reached the last 16.
Barty, troubled by a calf problem last week in Wuhan, said she felt no ill effects in a 6-4, 6-2 win over Kazakhstan's Yulia Putintseva.
The 21-year-old Japanese Osaka ruthlessly blew away Germany's Andrea Petkovic, 6-2, 6-0, in just 59 minutes.
The Dane Wozniacki defeated Christina McHale of the United States, 6-4, 6-0.
Back to winning ways
World number one Novak Djokovic, meanwhile, displayed steady recovery of his left shoulder injury on Tuesday by defeating an Australian challenger at the Japan Open, his first competition since pulling out of the US Open.
The experienced Serbian top-seed claimed a 6-4, 6-2 victory against 20-year-old Alexei Popyrin, who fought bravely at the Ariake Colosseum.
Djokovic nailed seven aces, against eight by Popyrin, and managed to win points on 84 percent of his successful first serves.
He finished the roughly 90-minute match by winning the final five games straight.
It was Djokovic's first singles competition since he withdrew from his US Open fourth-round match against Swiss Stan Wawrinka due to a left shoulder injury.