In ambient temperatures reaching 39 degrees Celsius, Murray conceded just eight games in putting away 100th-ranked Sousa, 6-2, 6-2, 6-4 in one hour and 41 minutes at the Hisense Arena, reports Xinhua.
"It's tough to get used to these conditions and it was extremely tough out there, and it was good to get it done in three sets," said Murray, who trained in Miami for playing in Melbourne.
Murray, who was the first Briton to win a Grand Slam in 76 years and also a twice runner-up at the Australian Open, dropped only seven games in his opening match against Robin Haase of the Netherlands.
The third seed will next play qualifier Ricardas Berankis of Lithuania, who was his practice partner when he won the lead-up Brisbane International two weeks ago.
