The British No 1 beat his upcoming opponent Kyrgios to reach the Australian Open semi-finals, and has set up a clay court contest after battling through some rough moments against Sousa to win 6-2 4-6 6-4 6-1.
Murray dropped a set to Sousa on Thursday but raced through the fourth set after breaking his opponent???s admirable resistance.
He started perfectly, forcing four break points in a marathon opening game before eventually breaking Sousa then holding to go 2-0 up.
Murray was moving through his own service games virtually unchallenged while heavily pressurising Sousa???s serve. With the world No 44 forced to defend from the back of the court, Murray broke a second time to go 5-2 ahead before easily finishing off the set.
Sousa, after such difficulties so far, offered no clue as to the comeback he would muster in the following set. Suddenly Murray seemed laboured and forced to battle through his own service games, while an overhand smash emphatically put Sousa 4-3.
With Murray briefly out-of-sorts, he lost his serve allowing Sousa to serve out the set and draw level. In 14 career sets between the pair, it was the first that Sousa had won.
Murray???s serve still wasn???t his ally into the third set and he narrowly saved a pair of break points to make it two games apiece. A burst of energy, the sort that remained above Sousa???s limits, enabled a Murray break for 4-3 and, two gradually improving service games later, he took the third set.
Sousa???s willpower and physical limitations seemed to have been reached and Murray hurried through a fourth set, breaking in the first game with a forehand winner and then again to move 4-0 ahead. A brief reply was offered before the world No 3 wrapped up the match in two hours and 31 minutes.