Rafael Nadal, 30, converted all three of his break points to end Sock's challenge in one hour and 20 minutes and set up a meeting with Austria's Dominic Thiem - a rematch of the Madrid Open final that the Spaniard won to enter the world's top four.
Nadal has won all 17 matches he has played on clay this year, winning the titles in Monte Carlo, Barcelona and Madrid.
World number two Novak Djokovic, 29, broke clay-court specialist Bautista Agut in the seventh game to take the first set before also breaking the Spaniard early in the second set. Switzerland's Stan Wawrinka had no answer to the impressive serving of Isner, losing a first-set tie break 7-1 before falling to a straight-set defeat.
Bautista Agut broke back and won three straight games, with Djokovic involved in an angry exchange with the umpire after being given a time violation.
However, the French Open champion rallied to reclaim the break and close out the match to set up a quarter-final against Argentina's Juan Martin del Potro, who saw off Japan's Kei Nishikori 7-6 (7-4) 6-3.
Thiem, 23, saved three match points to overcome American Sam Querrey 3-6 6-3 7-6 (9-7).
Unseeded John Isner sent down 19 aces and landed 84% of his first serves as he set up a last-eight tie against Croatia's Marin Cilic, who beat Belgium's David Goffin 6-3 6-4.
Earlier, Germany's Alexander Zverev secured a 6-1 6-1 victory over Italy's Fabio Fognini, who beat world number one Andy Murray in round two. Zverev will face fifth seed Milos Raonic in the last eight, after the Canadian beat Czech Tomas Berdych 6-3 6-2.
