Bautista Agut then scored his first win, upsetting Djokovic in the Shanghai semifinals.
After a quarter-final defeat by Dominic Thiem last year, Djokovic returned to Roland Garros not expected to challenge for the title following a year disrupted by an injury which needed surgery after the Australian Open in January.
The two players shared six breaks of serve during a back-and-forth third before Djokovic took a tie-break 7-4, but it was one-way traffic during the fourth.
The 30-year-old put up a real fight during a 4-6 7-6 (8-6) 6-7 2-6 loss to the former world No. 1 - a match that lasted the best part of four hours - but ultimately came up short.
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"Me and my brother (Mischa) are guys that spend three, four hours a day in the gym, lifting heavy weights, on the treadmill".
"I have been many, many times in quarters of Roland Garros and all the Slams, and of course I do appreciate it, considering it's a different kind of situation for me". That included their first match which was contested in 2013 in Dubai with Djokovic starting strongly in a 6-1 7-6 win.
"I think being able to win the first set and get ahead was crucial".
Thiem, the only man to beat Rafael Nadal on clay this year, held off a short-lived Nishikori revival on Court Philippe Chatrier to set up a clash with Zverev. The Dane barely dropped a sweat in her 6-0, 6-3 win to reach the Round of 16.
Shedding his mood lately in matches has been a very good signal for some onlookers - a sign that the starvation is again.More news: Duchess of Sussex: Meghan to accompany Queen for first time
Nishikori has twice reached the quarterfinals at Roland Garros, including past year.
"So they don't ask players whether we are the ones who are playing and sliding and not sliding, so we can give them the most important feedback".
The world number 13 put the hard circumstances to one side as he focused on beating Djokovic for only the second time in their eight meetings.More news: Tyson Fury confirms comeback fight - and sends warning to Anthony Joshua