Djokovic has yet to lose a set in the tournament and the 26-year-old was never in any danger against the 95th-ranked Sousa.
The 2011 US Open champion faced just two break points on his own serve as he raced to victory in 100 minutes.
“Just doing my job, win in straight sets and spend as less time on court as possible,” he said.
The Serb’s next opponent is Marcel Granollers, one of four Spaniards in the men’s last-16, who knocked the last US men’s player out when he edged wild card Tim Smyczek 6-4, 4-6, 0-6, 6-3, 7-5.
Bob and Mike Bryan did give the US’ men some cheer when they stayed on course to achieve a rare calendar-year Grand Slam in doubles after coming back to beat Canadians Daniel Nestor and Vasek Pospisil 6-7 (1/7), 7-5, 6-2.
The Bryan brothers have already won each of the last four Grand Slam doubles titles, starting with last year’s US Open, but are bidding to claim all four in the same calendar year.
The only men to have achieved the feat were the Australian pair of Ken McGregor and Frank Sedgman in 1951.