Murray had to fight on a couple of occasions but he generally looked in control as he progressed to the fourth round with victory over Querrey.
Buoyed by rival Novak Djokovic's surprise exit the day before Murray made sure there were no such shocks for him against the man who knocked Djokovic out of Wimbledon this year.
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Murray admitted that in the first set Querrey gave him a test but he felt he was on a roll after breaking back to take control of the set.
"It was tough," Murray said on court afterwards. "Especially in the first set, Sam was hitting a huge ball, he served extremely well but the key moment came at 3-4 in the first set.
"I saved a break point and broke the next game and had the momentum after that."
Speaking on Hisense, the first time Murray has played there this year, the world number one said "It was packed from the first ball and we love that as players,
"It makes for a great atmosphere. I really enjoyed being back here again on Hisense."
There were early concerns about his ankle, which he rolled during the game against Andrey Rublev, but afterwards he looked untroubled.
Speaking about the injury Murray said "I felt better and better as the match went on in terms of movement.
"I was a bit hesitant at the beginning, a bit sore, but was moving well at the end so that was very positive."
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