The 28-year-old came through in four sets 6-2 3-6 6-2 6-2 with victory marred by news that his father-in-law Nigel Sears had been taken to hospital after collapsing in the Rod Laver Arena.
Sears coaches Ana Ivanovic and was watching her match against American Madison Keys when he collapsed – though Jamie Murray confirmed he was ‘conscious, talking and sitting up’.
World No2 Andy Murray was unaware of what was unfolding while on court as he comfortably took the first set before losing his rhythm in the second.
He came back strong though and broke Sousa twice in the final set to take victory and set up a clash with either Bernard Tomic or John Millman.
“It was tricky. I didn’t feel I was in a great rhythm and wasn’t hitting the ball cleanly at the start. He was hitting the ball great, close to the lines, and making me do a lot of running,” said Murray in a statement after his press conference was cancelled and he left to visit Sears.
“Once I started to hit the ball a little bit cleaner towards the end of the match I was able to get him in his backhand corner and dictate more of the points.
“I just tried to keep fighting. At the end I was actually hitting the ball well and felt better at the end. It was good to get through that one.”
Elsewhere, Johanna Konta became the first British woman to reach the fourth round of the Australian Open in 29 years as she cruised past Denisa Allertova.
Konta won 6-2 6-2 in Melbourne – to match her run to the last 16 of last year’s US Open – and will now face 21st seed Ekaterina Makarova on Monday.
No British woman has made it this far since Jo Durie and Anne Hobbs in 1987 but the 24-year-old dominated with a first-serve percentage of 72 per cent and consistently created chances to break the Czech.
She wrapped up the one-sided win in just 66 minutes but claims it wasn’t as simple as it may have appeared at Melbourne Park.
“It was not easy out here today – she’s an incredibly tough opponent and I had an incredibly tough match against her at the French Open last year,” said Konta.
“I knew I really had to run down every single ball and fight every single point. So I’m happy that I did that. It definitely wasn’t easy.
“I’m feeling pretty good – it’s amazing what adrenaline does. You guys [the crowd] give so much energy to us that it makes it a pleasure to play. It really wouldn’t be the same without a crowd.”
Meanwhile a pair of Brits are on a collision in the third round of the men’s doubles as both Jamie Murray and Dom Inglot picked up second-round victories.
Murray and his Brazilian partner Bruno Soares beat Poles Mariusz Fyrstenberg and Jerzy Janowicz 7-5, 6-3 before Inglot and Sweden’s Robert Lindstedt saw off Americans Eric Butorac and Scott Lipsky 7-6 (7-5), 6-7 (5-7), 6-4.