Bautista Agut's previous win against Djokovic came two years ago in China.
The 30-year-old also has an outstanding record on Stanley Street.
Nole will face Roberto Bautista Agut in the semifinal.
"He played really well, smart, changing up the rhythm and the pace of the ball and moving me around.I was kind of in a corner and I had to find my way and fight my way through".
" I knew that he's playing probably the tennis of his life in the past 10 months, and he's definitely one of the greatest hitters in the game".
World No. 1 Novak Djokovic won another grueling battle in Doha on Thursday to continue his unbeaten start to the year and progress to the Qatar Open semifinals.
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" But I can not be more happy than I am now". Novak was up and it was tough. "I did everything well today".
Everything looked to be going to plan for Djokovic when he took the opening set in less than 40 minutes, however his opponent grew in confidence and went on to secure a first win over the Serbian since 2016.
By contrast, Bautista Agut had a comparatively simple straight sets win over former Grand Slam champion Sam Wawrinka, beating the Swiss 6-4, 6-4.
Djokovic was in cruise control in the first set, winning 6-3, and took an early break in the second.
After losing the first set on Friday evening, the seventh-seeded Spaniard prevailed in the tie-break to take the second set and began the third by breaking Djokovic's serve, reports Efe news.
Including the meeting with Bautista Agut, Djokovic spent nearly 10 hours on court in three days, and played 11 sets in singles' matches. "In conditions like this, it's quite suitable to him", Djokovic said of Bautista Agut.