World number 72 Marco Cecchinato stunned Novak Djokovic in a French Open classic on Tuesday to set up a semi-final clash against Dominic Thiem, with Sloane Stephens and Madison Keys to meet in the women's last four.
However, Bautista Agut - seeded 13th - hit back, grabbing a break of his own before staving off three set points and prevailing in a tense tie-break thanks to an error from his opponent.
Keys, the US Open runner-up to Stephens past year, will face Kazakhstan's Yulia Putintseva for a place in the semi-finals, after the world number 98 saw off Barbora Strycova 6-4, 6-3.
'I think that's going to be the No. 1 priority for me now to kind of step out from the tennis for a little bit, try to watch some matches and sort of try to progress somehow and just get better.
The 31-year-old also needed a medical timeout to treat a neck injury which looked as if it would derail him when he slipped 0-2 down in the second set to the Italian outsider.
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A tight first set heated up in the 10th game when Zverev saved two set points, the second after becoming incensed when the umpire overturned a line call of out from a Khachanov shot.
"Just a pity that I couldn't capitalise on the chances in the 4-1 in the fourth set and some break points".
The 20th seed reached the last 16 - where he will face Fernando Verdasco - at Roland Garros for the 12th time in his career after triumphing 6-4 6-7 (6-8) 7-6 (7-4) 6-2 on Suzanne Lenglen. I'm very happy because it's unbelievable to beat Novak Djokovic in a quarter-final at Roland Garros.
Dimitrov took a 3-1 lead in the tie break, but he eventually lost six out of the next seven points to fall one set behind.
Three-time champion Williams is playing her first Grand Slam tournament since taking time off last year due to pregnancy, while Sharapova is at Roland Garros for the first time in three years after serving a doping ban in 2016 and being refused a wildcard 12 months ago.
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The Bulgarian won the ATP Tour Finals in London past year but his wait for a grand slam title will go on after a 7-6 (7-4) 6-2 6-4 loss.
His hunger for the fight was clear for all to see too against Cecchinato in a thrilling tiebreak - the Serb roaring to the crowd, who chanted "Djoko Djoko" at crucial moments.
"I definitely thought about it, but I didn't want to pull out for the first time of my career in a Grand Slam quarter-final", said Zverev.
"Well, I'm young, so I might as well stay on court, get some practice and entertain you guys", smiled Zverev, who is bidding to become the first German man to win the French Open since 1937. 'Obviously I really expected to play better on clay.
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