The eighth-seeded Nishikori had a 7-6 (6), 6-1, 6-2 win on Margaret Court Arena right after Naomi Osaka's three-set comeback win over Hsieh Su-wei.
Nishikori, the 2014 U.S. Open finalist, fended off 59 aces from 39-year-old Ivo Karlovic in the second round before winning the fifth-set tiebreaker 10-7.
Sousa had also advanced through two five-setters and needed a medical time out in the third set.
The last time Nishikori won consecutive matches in five sets at a major was at the U.S. Open in 2014, when he beat Milos Raonic and Stan Wawrinka in five on the way to his semifinal win over Novak Djokovic.
It was Nishikori's third straight game on Margaret Court Arena, and he said he enjoyed the vibe — particularly after playing after fellow Japanese player Osaka, the U.S. Open champion.
"Forehand has been working very well. Second and third sets I was playing really aggressive, and everything was working well," he said.
He has reached the fourth round in Australia for the seventh time and is on a roll after winning the season-opening tournament in Brisbane.
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