Bacsinszky, who has reached the French Open semi-finals for the second time, made the last four in 2015.
Ramos-Vinolas immediately broke the Djokovic serve and might have led 3-0, but Djokovic pulled back to 2-2 before trailing again.
"I'm sure Wimbledon's on top of that stuff", said Britain's Jamie Murray, the brother of No. 1-ranked Andy Murray.
Since completing his career Grand Slam at the French Open 12 months ago, Djokovic has participated in four majors in a row without earning a trophy.
Nadal was leading 6-2, 2-0 when Carreno Busta retired after suffering abdominal injury.
"It's hard to comment (on) the third set". It's only the second time Djokovic lost a final set by the score of 6-0 in his 937 career tour-level matches.
She only needed one, winning with a crosscourt forehand victor.
Added Wozniacki: "I think they are, here and (in) the United Kingdom, trying to do everything they can to keep the security at the highest level, and I think here they are doing a good job".
The nine-time champion took the first set comfortably 6-2 before his Spanish compatriot took a medical time-out and returned to the court with strapping to his abdomen.
Plus, Djokovic had appeared in a record six consecutive semifinals in Paris. Djokovic enlisted Andre Agassi for coaching help during Week 1 of the French Open, but Agassi had some prior commitments and so was gone by the time Djokovic faced Thiem. No. 20 Pablo Carreno Busta, and Djokovic vs.
Heading into the French Open, many figured the women's draw was wide open, because of the absences of Williams' sister, Serena (who is pregnant), and Maria Sharapova (who was denied a wild-card entry that she needed as she comes off a drug suspension).
"I mean, it's a joke how tough it is to win a Slam", said Thiem, the only player who beat Nadal in one of his 23 clay-court matches this season.
Shortly before play is supposed to start, the temperature is 57 degrees F (14 degrees Celsius).
"Now it is the quarters in a grand slam and facing Dominic is not easy", the world number two said.
The last two women's quarterfinals are also on the schedule: Karolina Pliskova against Caroline Garcia, and Simona Halep against Elina Svitolina.