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It was an impressive start from the Wimbledon champion, who grabbed two early break points and put Robert on the backfoot almost instantly.
The Scotsman continued his dominance on the court in the Hisense Arena by grabbing a one-set lead over his French opponent in 25 minutes.
Nine winners and another two break points in the second set ensured that Murray had full control of the contest as he wrapped up the second set in 39 minutes.
However, Murray's plan fell to pieces in the third set as Robert launched a comeback by grabbing a break of his own, while the Scotsman relinquished six break points throughout the set.
A tie-break was needed to decide the third set, but it was Robert who came out on top 8-6, resulting in Murray losing his first set in the competition.
Despite the wobble, it was business as usual in the fourth set as Murray grabbed two break points to resume control, while Robert appeared to be struggling slightly with an injury.