After Djokovic won an opening-set groundstroke battle with steady accuracy and well chosen forays to the net, Bautista Agut used his big forehand to come back from 4-2 down in the second and win the next four games to level the match.
The world No 1 smashed his racquet after losing the second set but made better use of its replacement, winning the third following a service break in the fifth game, before raising his performances in the fourth set to claim victory.
"Congratulations to Bautista for hanging in there, for fighting. It was a great match tonight," said the Serb, winner of this year's Australian Open and Wimbledon titles.
The Spaniard unleashed 34 winners, including 22 from the forehand, but came up short in a quest to reach his first grand slam quarter-final.
"He made me work for every point," said Djokovic, who will meet Spain's Feliciano Lopez, who beat Italy's Fabio Fognini 6-3 7-6(5) 6-1, in the quarterfinals.
Only Jimmy Connors (27) and Roger Federer (36) have registered more consecutive grand slam quarter-final appearances in the Open era.
