The 35-year-old Scot defeated his fellow three-time Slam champion 7-6 (7/3) 5-7 7-5 in just under three hours in Cincinnati to progress to the second round.
Murray will now take on the British No 1 Cameron Norrie in the second round, which will be a stern test of the former World No 1’s credentials.
Norrie reached the semi-finals of Wimbledon during the summer and is one of the best players in the world on an American hard court.
When is Murray v Norrie?
The second-round tie in Ohio is due to be played on Wednesday. Murray v Norrie is first on Centre Court and starts at 4pm BST.
Is Murray v Norrie on TV? Is there a live stream?
Amazon hold the UK broadcast rights for the ATP main tour events and they will be showing the match on their Prime Video platform. Subscriptions cost £8.99. Alternatively, tennisTV show all the Masters 1000 series matches live and you can subscribe here.