The Serb, seeded ninth in the ongoing Masters 1000 tournament, needed 10 match points to register a 7-6 (2), 7-5 win over Coric. Djokovic had said he was playing without pain on his injury-prone wrist for the first time in two years after his win over Lajovic, and the way he fired some forehand winners Wednesday was a testament to his statement.
The world No. 1, chasing a remarkable 11th title in Monaco, got on top early against the young Russian and never looked like loosening his grip as he forced the 21-year-old into submission.
It was Thiem's second victory over Djokovic, adding to his 7-6 (5), 6-3, 6-0 win in the 2017 Roland Garros quarter-finals.
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The top-ranked Nadal beat big-hitting Russian Karen Khachanov 6-3, 6-2 on Friday to reach the quarterfinals, clinching victory with a clinical smash at the net.
Thiem should provide a sterner test in the last eight, after the fifth seed came from a set down to beat Djokovic.
"But it's the ultimate challenge for everybody, to play against him".
However, he was outclassed in the second set and seemed to fade physically in the decider, Thiem claiming his first break point for 4-3 and taking Djokovic's serve again to win after nearly two and a half hours.
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Djokovic admitted that he is still finding his way back to full fitness, although he did say he is playing pain-free for the first time in two years. "I'm pretty sure that we're going to see him at the very top of the game pretty soon". I have to rise my level again. "I think I'm able to do that".
Home favourite Richard Gasquet ran out a comfortable 6-2 6-1 victor against Argentine Diego Schwartzman, while German Philipp Kohlschreiber, Italian Andreas Seppi, and 14th seed Milos Raonic also all progressed to the last 16.
Third seed Alexander Zverev beat Jan-Lennard Struff 6-4 4-6 6-4 but missed out on facing his older brother Mischa Zverev in the last eight, who lost 6-2 7-5 to Frenchman Richard Gasquet.
Roberto Bautista Agut was not happy after dropping his serve in the second set against David Goffin and he hit a ball into the ground in frustration, unknowingly sending it into the direction of a ball boy.
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But Goffin broke again and served out the match at the third attempt to book a quarter-final against Bulgarian fourth seed Grigor Dimitrov, who beat Germany's Philipp Kohlschreiber 4-6 6-3 6-4.