In the second semi-final No. 4 seed Marco Cecchinato from Italy will take on Czech wild card entry Tomas Berdych.
This makes him a unsafe opponent for Djokovic, although it should be pointed out that their other three meetings on hard courts have all ended in favour of the Serbian.
The world number 24 triumphed in one hour 55 minutes in Doha to claim his ninth ATP Tour title.
And the world number one would seal his success with a game won to love, Basilashvili whipping a forehand wide and long as Djokovic's endurance in a lengthy rally once again proved the difference. So many times I found myself in defense.
"What happened? I lost the match".
It was clear that things changed on court in the second part of the opening set, and Novak started strong the second. Novak was up and it was tough. He was very solid and I had to play very good tennis. "I had to play a lot of lines and serve well". "I did everything well today".
The world No 1 fell to his first defeat of the new season in a high-quality contest lasting more than two-and-a-half hours, 6-3 6-7 (8-6) 6-4. He hasn't dropped a set this week.
Djokovic needed a decider to overcome Marton Fucsovics on Wednesday after dropping the opener and he was broken twice early on in the first set as Basilashvili took charge.
Djokovic broke the Spaniard in the second game of the first set to take a 2-0 lead.
Djokovic v Bautista Agut - Who will Win?
On serve there was little the Spaniard could do to unsettle his opponent, Bautista Agut only managing to take six points off Djokovic as the Serbian sealed the set easily.