Murray will play Alejandro Falla for the second time
Andy Murray survived a second-set wobble to beat Tim Smyczek 6-1 4-6 6-2 and book his place in the Farmers Classic quarter-finals in Los Angeles.
In his first event since Wimbledon - and first since splitting with coach Miles Maclagan earlier this week - the Scot showed signs of rustiness.
He struggled with his serve as he lost the second set before composing himself to seal victory in the third.
Murray will face Colombia's Alejandro Falla for a place in the semi-finals.
"Tonight was a very good match with a lot of long rallies, especially in the first two sets," said the British number one. "It was a good standard and hopefully it will stand me in good stead."
came close to beating Roger Federer at Wimbledon
beat fifth seed Ernests Gulbis 4-6 6-3 7-6 (10-8) earlier in the day.
Murray got off to the best possible start as he held then broke his American opponent to take a 2-0 lead.
He kept up that pace to power through the first set and never faced a break point.
Things got tougher from there, however, as Smyczek fashioned three break points in game four of the second set and duly converted for a 3-1 lead.
Murray broke back immediately and held for 3-3, but the American did not roll over and again established a two-game lead at 5-3.
Again the Scot broke back, but with his first-serve percentage for the set down to 42% he allowed Smyczek to level the match.
The contest continued in topsy-turvy fashion at the start of the third as the pair traded breaks in the opening two games.
Murray, who announced he was parting company with coach Maclagan on Tuesday, broke again for 2-1 and finally held to give himself a two-game cushion.
From there he did not look back and broke again for a 5-2 lead before serving out for a win which he may consider was more difficult than it needed to be.
"I was stiff, maybe because it was cool this evening," admitted Murray. "It's the first time I have played since Wimbledon. Hopefully I will be OK tomorrow."
Murray will take on Falla at around 0330 BST on Saturday, with the pair set to meet for only the second time after the Briton beat the world number 65 at an ITF event in the US in 2005.
"I actually played him in a Challenger in Binghampton,"
Murray told his website.
"It was in the final there when I was 18. He's a really nice guy and hopefully it'll be a good match."