The top seed and world No 2 was back on the court on Wednesday, just 72 hours after winning the gold medal in the men's tennis tournament at the Summer Games.
At one point during Wednesday's match Murray was treated by the trainer for a right shoulder problem.
He next plays South African Kevin Anderson, who beat French 13th seed Richard Gasquet 6-2, 6-4.
"I've played a lot of tennis, the balls are also different here," Murray said. "It's a quick turnaround and not really much time to adjust from Rio."
Second seed Stan Wawrinka polished off a two-day victory as he takes aim at a return to the year-end season finals in London.
