World No 1 Djokovic was the favourite to win the ATP 250 event and stormed his way into the semi-finals.
"Long matches today, both singles and doubles, and I spent quite a bit of time on the court but I'm happy I managed to get two wins", said Djokovic.
The defeat is Djokovic's first in 2019 and means Bautista Agut will face either Tomas Berdych or Marco Cecchinato in Saturday's final. From that moment I started to check all the possible stats and the stories behind the tennis players.
"I wasn't the freshest, you know". That's why Novak is number one in the world.
Speaking on court after the match, Djokovic praised fifth-seeded Basilashvili, who he had anticipated would provide him with a stern test.
The Serb cruised through the opening set before Bautista Agut dragged the contest into a decider by edging the tiebreak in the second set.
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'He played a good game.
"I wanted to give everything I had in the match and fight until the last point", Bautista Agut said. "He has a very physical style of Tennis which obviously is putting a lot of load and pressure on his joints, on his knees".
The Wimbledon champion, Djokovic lost the match by 3-6 7-6 (8-6) 6-4.
Djokovic lost two of his first three service games against Basilashvili and dropped the first set, as he had done in his last-16 win over Marton Fucsovics on Wednesday.
While in the first set, Djokovic was the dominant partner dictating terms, in the second it was Bautista Agut who pushed the top seed on the defensive.
Bautista Agut took their match in straight sets, going 6-4 6-4 over Stan the Man.
When Bautista Agut broke back for 4-4, the Serbian was furious and lashed out.