Jacks chalked up 10 sixes in his blitz as he put on an unbeaten stand of 166 with Virat Kohli, who hit 70 and remained in awe of his younger partner's hitting at the world's biggest cricket stadium in Ahmedabad.
Chasing 201, Benagluru achieved victory with four overs to spare when Jacks hit the winning six, which also made his century.
It was Bengaluru's third win -- and second in a row -- in 10 matches so far this season, keeping their slim hopes of reaching the play-offs alive.
Jacks was on 16 when the in-form Kohli reached his fifty in 32 balls with a four off Rashid Khan, but soon the 25-year-old Englishman exploded with three sixes and two fours in a 29-run 15th over from Mohit Sharma.
"Phenomenal. Initially when he came to bat, he was annoyed that he wasn't able to strike the ball as he wanted to," Kohli said after the win.
"The only talk was for him to stay calm; we know how explosive he can be when he gets going. The over from Mohit was the game changer, I was just happy to stay around and watch him go."
Jacks then took on Rashid with four sixes and a four in the winning over.
The 35-year-old Kohli, who hit the first ton of this edition, reached 500 runs and was quick to slam critics who said the veteran batsman has struggled to meet modern T20 standards of power hitting.
"There's a reason why you do it for 15 years. For me, it's only about doing the work. People can talk anything they want to, they can talk about me not able to push on, not playing spin well, but you yourself know the game better," Kohli said.
On Bengaluru's disappointing showing this season, he added: "We wanted to play more for our self-respect, we want to play for the fans who have backed us. We know we haven't played up to the standards required. We know we can do a lot more better and it's something which we'll try and do."
Kohli -- who played the spinners with aplomb, including by using the sweep shot to good effect -- and Bengaluru are still waiting for their first IPL title.
Bengaluru, who remain bottom of the 10-team table, elected to field first and Gujarat reached 200-3 in their 20 overs.
Sai Sudarshan hit an unbeaten 84 and put on key partnerships, including putting together 86 runs with Shahrukh Khan, who hit 58, and an unbeaten 69-run stand with David Miller, who made 26.
Glenn Maxwell returned to the Bengaluru XI after a short "mental and physical break" break of three matches, taking a wicket in his first over to return figures of 1-28 with his off-spin.
