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.
"Tough, very tough match for me," Murray, who missed the 2013 French Open with a back injury, said.
"I played him once before on clay and I think I got three games or something."
Wimbledon champion Murray was inevitably quizzed yet again on who would be his next coach following his split with Ivan Lendl.
"There have been a lot of different names that people mention," Murray, who seems to be doing perfectly well on his own, said.
"Obviously Amelie (Mauresmo) this week, there was (Mats) Wilander, there has been (Jonas) Bjorkman, John McEnroe, (Martina) Navratilova, Leon Smith, who is the Davis Cup captain, Bob Brett.
"I have a good relationship with most of them. Some of them I don't even know. So, yeah, no bad names there."
"When the time is right I will make an announcement."
The mention of Mauresmo's name in connection with the Murray coaching job set tongues wagging in the French capital, and Murray did not discount the possibility that Lendl's successor could be female.
"For me, I don't care," he said. "I don't really care whether some of the other male players like it or not. That doesn't - that's not something that really bothers me.
"I was coached by my mum (Judy) for a long time. I have had her around at tournaments for a long time. There has been ex-players and stuff that have said, Oh, your mum shouldn't be around or she shouldn't come and support you or come to watch.
"It's silly. Everyone is entitled to have the team around them that they want. Everyone works very differently.
"Some men might not work well with a female. Some men might work well with a female coach.
"It's just whatever your preference is and whatever your needs are."
Round 2 results:
1-Rafael Nadal (Spain) beat Dominic Thiem (Austria) 6-2 6-2 6-3
5-David Ferrer (Spain) beat Simone Bolelli (Italy) 6-2 6-3 6-2
7-Andy Murray (Britain) beat Marinko Matosevic (Australia) 6-3 6-1 6-3
19-Kevin Anderson (South Africa) beat Axel Michon (France) 6-2 6-3 6-2
Donald Young (U.S.) beat 26-Feliciano Lopez (Spain) 6-3 7-6(1) 6-3
28-Philipp Kohlschreiber (Germany) beat Denis Istomin (Uzbekistan) 6-3 7-6(5) 6-2
32-Andreas Seppi (Italy) beat Juan Monaco (Argentina) 6-2 6-4 6-4
Leonardo Mayer (Argentina) beat Teymuraz Gabashvili (Russia) 6-2 4-6 6-4 6-4
Guillermo Garcia-Lopez (Spain) beat Adrian Mannarino (France) 6-4 6-3 4-6 6-0
Dusan Lajovic (Serbia) beat Juergen Zopp (Estonia) 6-2 6-4 6-4
Ivo Karlovic (Croatia) beat Andreas Haider-Maurer (Austria) 7-5 6-3 6-4
Jack Sock (U.S.) beat Steve Johnson (U.S.) 7-5 6-4 6-2
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