Had Djokovic won, he would have faced Rafael Nadal on Friday in the quarter-finals - and thus set up the first meeting between two members of tennis's elite group since Nadal lost to Roger Federer in October's Shanghai final.
Positive signs for Djokovic despite defeat Djokovic has slipped to 13th in the rankings as an elbow injury has restricted him to only four tournaments this year, but he showed glimpses of his best form against Thiem, whom he described as a "top-three player in the world on clay".
Thiem beat Djokovic in straight sets in the French Open quarterfinals previous year including 6-0 in the third but Djokovic won their other five meetings.
Hindered by a persistent right elbow injury, Djokovic says he is finally pain-free for the first time in two years and a little rusty.
The 16-time Grand Slam victor, like Djokovic, is looking for a record 31st Masters title, and he swatted aside Bedene for the loss of only four games.
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[ALSO LIKE] Thiem, well versed in long, lung-testing rallies on red dirt, saved one break point in his first service game, then played a patient game at 2-2, when Djokovic recovered from 15/40 only to hand the Austrian a break with a backhand error. "That's the real thing", said Nadal.
"It's way better feeling if you go contrary to him (Nadal) and be aware you've conquered him on the particular surface", the 24-year-old Thiem explained.
The match lasted more than two hours, and Djokovic, playing in only his fourth tournament since last summer's Wimbledon championships, required 10 match points to get his victory over the line.
"It's the ultimate challenge to play against him".
The Spaniard got on top early, breaking to love on his way to a 3-0 lead and despite a brief blip on serve at 4-2, he broke once more to wrap up the opener. "I think I'm able to do that".
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Third seed Alexander Zverev also fell behind to Luxemburger Gilles Muller, before coming through 4-6, 6-3, 6-2.
Second seed Marin Cilic is also into the last eight, after Milos Raonic pulled out with a right knee injury before their third-round match on Thursday.
Goffin is to play against either Philipp Kohlschreiber of Germany or Grigor Dimitrov of Bulgaria, while Zverev is set to take on next either his brother Mischa or Frenchmen Richard Gasquet.
There were also round of 32 victories for Japan's Kei Nishikori after he clinched a 7-5 6-2 victory against Daniil Medvedev of Russian Federation.
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