Victory secured a fourth career title for Basilashvili.
The clash was characterised by hot, dusty wind that slowed down the exchanges but world No.42 Basilashvili bided his time to snatch the first set in a tiebreak.
Basilashvili, who arrived at the Qatar Open with a 2-13 record since the resumption of the sport in August, penetrated 2019 champion Bautista Agut's defences in the sixth game of the second set, winning a crucial breakpoint with a backhand.
He made simple work of the eighth game to win the trophy on his first championship point after 90 minutes on court.
"I had zero expectations to win the tournament," 29-year-old Basilashvili said.
"It was very tough conditions today it could have gone both ways."
The tournament will be mostly remembered for Federer's return to tennis after 13 months out to recover from knee surgery. He mustered a win again Britain's Dan Evans before falling to Basilashvili.
Federer, who has since pulled out of the Dubai event next week, now has his eyes firmly set on Wimbledon where he has won eight of his 20 Majors.
On Sunday (AEDT), the wind blew from left to right in the opening points, with Bautista Agut's opening serve given a noticeable swerve by the breeze.
Out-swing from Bautista Agut's forehand saw balls that would have ended up well inside the court under normal conditions touching the line.
The blustery night made play more tentative than in previous rounds with rallies noticeably slower.
Basilashvili moved to control the points early but nine holds of serve in the first set, and with the pair tied at 6-6, the set went to a tie-break.
He ground it out from the baseline with a backhand delivering him set point, overpowering Bautista Agut's slice backhand.
The second set was a simpler affair with the Georgian racing ahead to win the set and the tournament.
"Today it was his final," No.5 seed Bautista Agut said after his defeat.
"He played very aggressive and now it's time to recover... and hopefully come back next year and try to get the title again."
Qatar has pressed ahead with sporting events like the Qatar Open, which allowed spectators at 20 per cent capacity, despite seeing an uptick in coronavirus cases.
Spectators were required to present a contact tracing app, undergo temperature checks and wear masks at all times.