The comfortable victory came as a relief to the eighth seed and former U.S. Open finalist after he battled through consecutive five-set matches in the opening rounds.
"I think today will help," the three-times quarter-finalist said after setting up a clash with Spain's 23rd seed Pablo Carreno Busta.
Both Nishikori and Sousa entered their match after tight opening rounds and were evenly matched in the early exchanges on their favoured hard court surfaces.
But after a close tiebreaker, Nishikori took near total control, increasing the pace on his ground strokes and showing soft hands at the net; a quality his opponent couldn't replicate.
He said he would continue attacking the net after using the tactic successfully on Saturday.
"I think third set, I started coming (in) a little more, I think that was working well," said Nishikori.
A small pocket of red and green-clad fans added a football-like atmosphere to the clash as they cheered Portugal's top-ranked player.
But Nishikori robbed them of their voice, as he unleashed forehand winners almost at will, a stroke he said was his favourite shot despite being better known for his double-handed backhand.
Fittingly, the Michael Chang-coached Nishikori ended the contest with a clean, cross-court forehand winner to keep his hopes of a maiden Grand Slam alive.
(Reporting by Jonathan Barrett; Editing by Peter Rutherford)
