Spain's former champion Bautista Agut, the No.5 seed, eased past Russia's Andrey Rublev, ranked No.8 in the world and the defending champion, with a dominating performance, 6-3 6-3.
Fresh from a famous victory against Roger Federer, back after 13 months of injury absence, in the quarter-finals, Basilashvili edged American Taylor Fritz 7-6 (7-3) 6-1.
The 29-year-old will attempt to secure his fourth title on Sunday (AEDT) after saving a match point against Federer.
Bautista Agut, the 2019 Qatar champion, had already ousted Dominic Thiem, the No.1 seed, in the quarter-finals and powered on through the semi-finals.
Rublev had an unusually easy path to the last four, a first-round bye which was followed by injury-enforced walkovers handed to him by Richard Gasquet and Marton Fucsovics.
Bautista Agut had a difficult start to this season with four wins to five losses coming into Doha.
But it pales in comparison to the slump endured by his Georgian opponent, who arrived at the Qatar Open with a 2-13 record since the resumption of the sport in August.
"Yesterday's match already give me a lot of confidence," Basilashvili said of his victory over 20-time grand slam title winner Federer.
"Today I was much more relaxed than I was (in) I don't know... eight tournaments."
He described Bautista Agut as a "very good baseline player".
"He doesn't have many errors, so it's going to be tough match for me," he said.
Bautista, who celebrated his 14th top-10 win after ousting Rublev, described the Qatar Open and the Khalifa International Tennis Complex as "one of my favourites".
"I played one of my best matches here in Qatar two years ago, and I hope I can win one more match tomorrow," he said after his win.
"It was very difficult to play tennis today, with the windy conditions... but I put a lot of pressure on his second serve and played really good tennis.
"I played a long match yesterday, but I felt fresh and I had a lot of power on the court."