The pattern was set in the first game as Wimbledon champion Murray broke serve and he went on to dominate a player appearing in the second round of a grand slam for the first time.
Matosevic hung on grimly in the opening set and did have a chance to level when he was 0-40 ahead on Murray's serve in the eighth game but he failed to take his chance and was never close to his opponent again.
Briton Murray, who missed last year's French Open with a back injury, was broken for the first time when he served at 5-2 in the third set but hit back immediately with a love game to set up a clash with Germany's Philipp Kohlschreiber.
Bosnia-born Matosevic had defeated Dustin Brown in the first round to end a 12-match losing streak at the majors.
(Reporting by Martyn Herman, editing by Ed Osmond)
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