Murray wasted 10 break points before finally converting to take a 3-1 lead in the second set. He won his only other break point in the third set to take a 2-1 lead.
Later Monday, top-ranked Novak Djokovic was to face Jo-Wilfried Tsonga in the other Group A match at the season-ending tournament for the top eight players in the world.
Group B, which includes Roger Federer, will play Tuesday.
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