Ranked as the top two sides in the world, the pair remain on course to meet in the final on September 14 after comfortable victories in the round of 16.
Defending champions USA saw off Mexico 86-63 in Barcelona, thanks to 20 points from point guard Stephen Curry and despite the best efforts of Gustavo Ayon (25 points)
USA head coach Mike Krzyzewski, who oversaw the victorious campaign in Turkey in 2010, singled out centre DeMarcus Cousins for special praise after the victory.
"All the reports about him not making the team and all that were all not right," he said.
"We felt he would be the perfect guy with or in place of Anthony [Davis] at times, but more in the place of Anthony, and I think it's just a matter of him continuing to get in better shape, our guys getting accustomed that when he does come into the game he's different than Anthony and so to look for him.
"I think they see him more now, and I think his defence has really improved. He tried to take three charges today. He played Ayon pretty well without getting help, so they couldn't get a three off of him.
"I thought he played, not grading everybody although you guys do that, he'd get an A+ from me today, let's just put it that way."
USA now move into a quarter-final with Slovenia, who saw off Dominican Republic 71-61.
After a tight opening quarter, Slovenia pulled 10 points clear by half-time and were able to maintain that advantage throughout the remainder of the encounter.
Spain had little trouble in overcoming Senegal in their last-16 clash, cruising to an 89-56 victory.
They will now take on France in an all-European quarter-final, after Vincent Collet's men edged past Croatia 69-64.
Bojan Bogdanovic starred for Croatia with 27 points, but it was not enough to overcome the European champions as France advanced to a clash with the hosts in Madrid.