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In the second rubber of the day, Murray and Bemelmans both broke early in the first set, but the two-time Grand Slam champion showed his experience by snatching serve again to take a 4-2 lead.
After taking a one-set lead, Murray broke instantly at the start of the second set, and despite Bemelmans battling to create a break point of his own, his opponent was too strong.
Murray, who will play every day in the three-day contest, went a second break up before taking a two-set lead.
The start of the third went by way of serve as Bemelmans managed to save three break points before snatching Murray's serve to go 4-2 up, but the Scotsman instantly broke back.
During that spell, Murray dropped a point as a result of a warning from the umpire, while Belgium's coach was also warned for his conduct with the crowd.
Murray was able to recover, though, as he came from set point down to hold and then break immediately before seeing out the set and grabbing an all-important point for Great Britain.