Murray shows his class to beat fading Malisse
Murray, who had a first-round bye, was slow to start and found himself a break down at 3-1 in the first set.
But the Scot broke back to make it 5-5 before powering to take the set 7-5.
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Hide AdMalisse never regained his composure long enough to trouble the world No 4, who will face France's 15th seed Gael Monfils in the next round.
Roger Federer beat Juan Ignacio Chela to reach the third round – his first match since crashing out at Wimbledon in June.
Federer edged the first set against the Argentine before winning 7-6 (9-7) 6-3.