Chennai captain Ruturaj Gaikwad had won the toss and chosen to field but failed to capitalise as the Gujarat openers propelled the team to an imposing 231-3.
Chennai stumbled at the start of their innings and could only reach 196-8.
Chennai remain fourth in the table while Gujarat jump from last to eighth, keeping their hopes of qualifying for the next phase mathematically alive.
Gill and Sudharsan were quickly into their stride, racing to 58-0 in the first six overs of the game.
Sudharsan struck five fours and seven sixes in his 103 which came off just 51 balls.
Gill's 104 was marginally slower, coming from 54 balls, but included nine fours and six sixes as both openers savaged the Chennai attack.
"We maximised every over and opportunity in front of us," said Gill who was made player of the match.
Their partnership matched the IPL record for the first wicket set by KL Rahul and Quinton de Kock for Lucknow Super Giants against Kolkata Knight Riders in 2022.
They fell just short, however, of the overall IPL record of 229 posted by Virat Kohli and AB de Villiers for Royal Challengers Bangalore (now Bengaluru) against Gujarat Lions, the previous franchise to the Titans, in 2016.
Both openers fell in the 18th over to Tushar Deshpande, the only Chennai bowler who took wickets and finished his four-over spell with 2-33.
Indian rookie Shahrukh Khan (2), the only other Gujarat wicket to fall, was run out in the last over of the innings.
One of the pre-tournament favourites who are still in contention for the playoffs, Chennai got off to the worst possible start and lost both openers by the second over of the chase.
New Zealand international Rachin Ravindra (1) was run out by South Africa's David Miller in the very first over.
His opening partner Ajinkya Rahane fell to rookie Sandeep Warrier for one in the next over.
Chennai's in-form skipper Gaikwad lasted just three balls before hammering Umesh Yadav out to the square-leg boundary where Rashid Khan juggled the catch just inside the boundary, taking it at the second attempt as he stepped back inside the rope.
Gujarat were in deep trouble at 10-3 in the third over before all-rounders Daryl Mitchell and Moeen Ali salvaged the innings.
New Zealander Mitchell, who scored a 34-ball 63, and England's Ali, who hit a 36-ball 56, stitched a 109-run partnership.
They took the score to 119 before both were removed in successive overs from India pacer Mohit Sharma.
Sharma, who also removed the dangerous and in-form all-rounder Shivam Dube (21), finished his key spell with 3-31.
Indian all-rounder Ravindra Jadeja hit 18 and MS Dhoni chipped in with an unbeaten 11-ball 26 to take Chennai to 196-8.
