Sousa posed few problems to an in-form Murray on the Hisense court as the Scot claimed a 6-2 6-2 6-4 win in under two hours.
Murray had to deal with a match played in the searing Melbourne heat, with temperatures reaching 40 degrees.
The third seed declared that he was delighted with a strong serving performance which kept plenty of energy in the tank for tougher tests ahead at Melbourne Park.
He said: "I served well, which was important today as I didn't want to get drawn into two many long rallies.
"When I first came on the tour the humidity really got to me but now with my training in Miami I know what to expect.
"I'll head over now and use the ice baths at the National Tennis Centre, that's the best way to recover."
Murray will face practice partner Ricardas Bernakis in round three on Saturday.