Djokovic was also world number one at that stage.
Djokovic, who has now won 13 consecutive matches in Doha, told www.atptour.com: "I thought Basilashvili was playing terrifically from the beginning". Roberto, who had just one victory over the world number one, played some of the best tennis in his life to deny Novak Djokovic a title shot in the finals.
"I feel I have a gear or two up still". I know it's hard to play at this level. The Serbian has been nearly unbeatable on hard courts over the last six months, but Bautista-Agut trumped him in a tactical masterclass.
"So you kind of have to be alert at the same time when the chances present, to take control".
'I can't be more happy than I am right now'. "I managed to get a win, which is what matters".
The pair have met on 8 previous occasions, with Djokovic now holding a 7-1 lead in terms of matches won advantage.
Bautista Agut will rise one place in the world rankings to 23 on the back of the victory in Qatar, and said his aim was to go higher. "I had to play a lot of lines and serve well". "I think I did a very complete match".
The first win came in October 2016 in Shanghai.
"Tough opponent for sure".
By contrast, Djokovic's opponent in the semi-final is yet to drop a set this week. He played great today against Stan.
"I wanted to give everything I had in the match and fight until the last point", Bautista Agut said.
Not since Rosewall's progression to the 1977 final in Hong Kong has a player older than Karlovic vied for a title - and the Croatian will hope he emulates the Australian by going on to win on Saturday. "That's his strength. He always puts an extra ball in the court".
In the other half of the draw, wild card Tomas Berdych took only 71 minutes to dispense with Pierre-Hugues Herbert 6-2 6-4.