Still yet to drop a set in her five matches at Roland-Garros this year, the 23-year-old responded magnificently after a break left her two games adrift in the opening set, which she won via tiebreak after missing two set points.
Analyzing the match, Djokovic added: 'He played incredible and credit to him. "There was another year of work where I improved and developed my game", said the 24-year-old.
At 5-5 in the second set tie-breaker, a Djokovic volley deflected off the net and landed wide.
"I was a bit unlucky not to capitalize on the second set", said Djokovic, who improved to 7-1 against Bautista Agut.
Thiem reached his third successive French Open semi-final with a 6-4, 6-2, 6-1 demolition of a hobbled and exhausted Alexander Zverev who admitted he was close to quitting the tie. For me to beat Djokovic in a quarter-final at Roland Garros it's fantastic.
Zverev produced some stunning tennis in the closing stages of a dramatic fourth-round victory and will next face Dominic Thiem who reached a third successive quarter-final in Paris by seeing off Japan's Kei Nishikori 6-2, 6-0, 5-7, 6-4.
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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.
On Tuesday, he became the first Italian to reach the last four at a major in 40 years by beating 12-times Grand Slam champion and 2016 Roland Garros victor Novak Djokovic on Court Suzanne Lenglen.
"He is one of the fittest guys on the tour so it was hard for him today", said Thiem, the only man to have defeated 10-time French Open champion Rafael Nadal on clay this year.
"Is good for my opponent in Wimbledon", he said.
"I think it's changed my life".
Djokovic has been superb to this point at Roland-Garros, most recently defeating the streaking Fernando Verdasco 6-3, 6-4, 6-2 on Sunday.
Djokovic, bidding to reach a 32nd Grand Slam semi-final, hit just three winners in the first set. "Today, (that) I won this match is really incredible, reaching the semifinals I'm happy for having written a place in history". This will be Zverev's first quarterfinal match in a Grand Slam, so Thiem edges him in experience. "Now I beat David Goffin, (who) is one of the best players in the world".