All seven previous matches in the IPL between the sides had been won by the chasing team, and Gill therefore had little hesitation in asking Bengaluru to bat first at the Narendra Modi Stadium in Ahmedabad.
Virat Kohli smashed Kagiso Rabada for five fours in the second over of the match before succumbing to the same bowler not long thereafter as Bengaluru went from 79 for two to 155 all out.
Devdutt Padikkal top-scored with a fluent 40, while left-arm pacer Arshad Khan (3/22), Gujarat's most successful bowler, received excellent support from Afghan Rashid Khan.
West Indian Jason Holder had headlined a flawless first half for Gujarat with three catches to go with the wickets of Jitesh Sharma and Romario Shepherd, triggering a middle-order collapse which compelled Bengaluru to summon Venkatesh Iyer as the impact substitute.
"It was one of those nights (when the ball kept following me)," player-of-the-match Holder said.
"The energy was quite high. I am just happy to hold on to the chances and happy to help the team win."
Having deployed Venkatesh, Bengaluru found themselves a specialist seamer short, and Gujarat made them pay despite a wobble during the middle stages of the modest chase.
Bengaluru were heavily reliant on the seasoned new-ball duo of Bhuvneshwar Kumar and Josh Hazlewood to strike early, but Gill had other ideas.
The opener tore into Hazlewood, hammering the Australian for three fours and two sixes in the second over to give his team a strong start.
Bengaluru fought back through Bhuvneshwar, who accounted for Sudharsan and Gill after a sparkling 43, but Buttler kept up the momentum with a hat-trick of sixes in his knock of 39.
Bhuvneshwar returned for a one-over final spell during which he yorked Buttler for his 17th wicket of the season.
With their prolific top three back in the hut, Gujarat made heavy weather of the chase.
Shepherd, getting an extended bowl largely because Bengaluru didn't have a specialist third seamer, dismissed Shahrukh Khan and Washington Sundar in the space of three deliveries to spark some excitement, but Gill and Buttler had scored so rapidly that Gujarat didn't have to contend with run-rate pressure.
Rahul Tewatia held the second half of the chase together and Rashid struck the winning boundary with 25 deliveries to spare.