The Wimbledon champion would not have expected to have too much trouble against a player he had beaten easily twice before and so it proved as he wrapped up a 6-3 6-1 6-3 victory in an hour and 56 minutes.
Murray is likely to face a significantly greater test in the next round against 28th seed Philipp Kohlschreiber, who won their only previous match on clay four years ago.
The seventh seed had done enough in a four-set victory over Andrey Golubev in round one and was no doubt happy conditions were much warmer and drier on Thursday.
There was no sign courtside this time of Amelie Mauresmo, the former Wimbledon champion whose presence at Murray's victory over Golubev led to speculation she could be his new coach.
The match was played in the tight confines of the Court One bullring, and Murray made a fine start with a break of serve in the opening game.
The Scot was the first opponent Matosevic had ever faced in the second round of a grand slam, the 28-year-old having finally won a main-draw match on Tuesday at the 13th time of asking.
The Australian was given the nickname 'Mad Dog' at home and is known for his on-court antics, but he and Murray are good friends.
After a slow start Matosevic began to play better and put some pressure on Murray, and the British number one had to dig himself out of a hole down 0-40 in the eighth game.
Having come through that sticky moment, Murray then forced a set point on the Matosevic serve, which he took when his opponent sent a backhand flying long.
Both men had chances at the start of the second set but it was Murray who took his to lead 2-0.
A sense of order had been restored on Thursday after the big upsets of the past three days, and Matosevic had to save three more break points to prevent Murray moving 4-0 in front.
It was only a temporary reprieve, though, as Murray, who was killing the Matosevic second serve, broke again and then served out the set with a second-serve ace.
The third set started with the longest game of the match but after 16 minutes and five break points it ended the same way most of the rest of them had - with Murray winning.
Matosevic simply had nothing to really hurt his opponent with, and Murray took another long game to move 4-1 ahead.
The Scot wobbled slightly within sight of the finish line and Matosevic broke serve for the first time in the match, but Murray hit straight back and took his first match point, appropriately with a backhand return winner.