The Austrian began his tournament by defeating Ilya Ivashka of Belarus in straight sets 6-2 6-4 6-1.
"I'm young. I might as well stay on court and entertain you guys", Zverev, 21, joked with the crowd. "All the hours in the gym have paid off". "Maybe it's a dream, because now I'm very, very happy for this match".
Zverev said he spends up to four hours each day working on weights and fitness.
In a tight first set of a match played in overcast, heavy conditions, Thiem converted the only break point off a backhand victor in the seventh game before securing the opener with an ace.
"It's, I think, the match, especially in Germany and Austria, everybody was hoping for".
"I'm obviously a tennis fan just like everyone else, so I think I'm just as excited to see that match", said Keys. He chatted with himself during changeovers - "I like to talk", he said later - and dropping down onto the red clay after one last backhand victor on match point.
Nadal, meanwhile, is bidding for yet another win at Roland Garros.
Djokovic eased previous Fernando Verdasco 6-Three 6-Four 6-2, though the early phases on Philippe-Chatrier court docket instructed a prolonged battle. It's also Djokovic's 12th career trip to the quarterfinals in Paris, a record for the 50-year professional era.
"At the Grand Slams, there are the big four".
Thiem defeated Zverev in their first match which came in the Munich semifinals, with the Austrian's 4-6 6-2 6-3 victory making him the last man to defeat Zverev in Bavaria.
Zverev sank to his knees in celebration. He then patted Khachanov, a friend from their junior days, on the chest before pumping his arms to celebrate.
Zverev began to let rip, snatching one game back, but the outcome was inevitable and Thiem put him out of his misery with a routine backhand victor into a wide-open court. However, in the second round he was extended to five sets by Lajovic, eventually winning 2-6 7-5 6-4 6-1 6-2.
Putintseva made the first significant move with a break in the seventh game, but failed to serve out the set as Keys found her range.
Thiem broke in the first and third games, but Zverev showed his spirit, coming to the net to hold in the fifth game.
Khachanov had some chances in the second and again late in the match, but his forehand let him down.
The 13th seed admitted in the build-up that she had never watched Buzarnescu in action but quickly got to grips with the unheralded 30-year-old who was playing in the fourth round of a Grand Slam for the first time.
My model agreed with this line, and in short, I'd be utterly amazed if the former world number one was unable to extinguish the Italian's hopes of making his first Grand Slam semi-final, in what is his first Grand Slam quarter-final.
The 10th-seeded American had little trouble beating No. 14 Daria Kasatkina 6-3, 6-1.
It was the Serb's 200th Tour-level clay court match win.
"A hard one to swallow", Djokovic acknowledged during a brief news conference, in which he delivered clipped answers and said he might not play during the upcoming grass-court season.