Murray had played his first two matches on Margaret Court Arena and won both in straight sets to set up a third-round clash with Portugal’s Sousa, who knocked out 32nd seed Martin Klizan.
The sixth seed was required to switch to Hisense Arena on Friday but found the new surroundings equally to his liking with a convincing 6-1 6-1 7-5 victory.
Following a stuttering start, Murray pounced in the fourth game to break his opponent, whom he has beaten in all three of their previous encounters.
The Scot secured a double-break to make it four games in a row before serving out the opening set in 31 minutes on a packed Hisense Arena.
Two-time Grand Slam champion Murray started to produce an array of his best shots, flattening out his forehand and striking the ball beautifully.
He broke early in the second for a 2-1 lead and quickly backed up the break with his first love hold of the match before securing a double-break to move even further ahead.
And to make matters worse for Sousa, the 25-year-old looked in severe pain from an injury to his left knee when he received treatment at 4-1 down.
It was one-way traffic and the three-time Melbourne finalist wrapped up the set by forcing more errors off the racket of his opponent.
The world No 55 was able to continue and managed to win his first game in eight on serve at the start of the third set, but Murray broke once more in the fourth game to leave Sousa with a mountain to climb to maintain his record of never having lost a five-set match in a Grand Slam.
A lapse in concentration cost the sixth seed a break of serve and his 4-1 lead was wiped away. He failed to take advantage of two match-points at 5-4, but a more aggressive Murray got the job done to wrap up victory in a little over two hours.
Murray will next meet Dimitrov,??who ended Murray’s Wimbledon title defence in the quarter-finals last??year.
The 10th seed laboured to get past crowd favourite Marcos Baghdatis with the fired-up Cypriot pushing him to five tough sets.
Dimitrov looked to be heading for defeat when the 2006 Open runner-up won the third set before he rallied to claim an exhausting 4-6 6-3 3-6 6-3 6-3 victory??in a match lasting three hours and 28 minutes and played in a raucous atmosphere on court three at Melbourne Park.
Dimitrov, who reached the semi-finals at Wimbledon last year, said: “Obviously it was a tough game for me. I didn’t really feel comfortable on the court. I thought Marcos was playing dominating tennis early on in the match. I wasn’t really able to turn things around as fast as I wanted to.
“I felt quite good physically, which was I think the best sign for me today. I’m not going to hide my excitement of winning the match because it meant a lot to me. To be able to play three and a half hours and win 6-3 in the fifth and feeling really good after the match physically, that says a lot for me.”
It took Dimitrov’s record in five set matches to 4-3 and one that will prepare him against Murray in the next round.
“It’s a great matchup for me. I’m always excited to play against him. I had a tough loss against him in Paris and I always like that kind of challenge,” Dimitrov said.
“I think physically and mentally I’m ready to play that match and really give 100 percent. I’m going out there to win the match.”