The Portuguese was brushed aside 6-2 6-2 6-4 as the world number three advanced to a last-32 meeting with Ricardas Berankis.
Importantly, on the hottest day of the tournament so far - temperatures moved beyond 100F in Melbourne - Murray got the job done in just an hour and 41 minutes, conserving energy for what he hopes will be a concerted push for a second successive grand slam crown following his maiden major win at the US Open.
“It doesn’t matter how much training you do, it’s tough in these conditions,” he said.
“It’s extremely hot, especially when the sun comes through the clouds. It’s good to get it done in three sets.
“The longer the rallies go the tougher it becomes on the legs.
“You need to get in control of the points and dictate them because otherwise you will get very tired very quickly.”
The match itself was a no-contest, the outcome never in doubt with Sousa’s game simply not big enough to cause Murray any significant problems.
The world number 100 had limited chances to impress as Murray dictated the match from the baseline.
And on the rare occasion he had to escape from trouble, the Scot’s serve came to his aid.