The second seed, chasing a seventh title in Halle, squandered five break points in the first set against the 47-ranked Sousa.
But Federer, who was beaten in the fourth round of the French Open by Ernests Gulbis, ran out a comfortable victor after easily winning the next two sets.
Federer will face either towering Croat Ivo Karlovic or Lu Yen-hsun of Taiwan for a place in the semi-finals.
Rafa Nadal will be dusting off his claycourt shoes after winning his ninth French Open title on Sunday when he begins his grasscourt campaign against maverick German Dustin Brown.
(Writing by Pritha Sarkar in London, editing by Martyn Herman)
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