Chennai were almost denied by medium-pacer Mohit Sharma in the final over, moving from favourites to needing 10 runs off the last two balls.
But Sharma got his length wrong and Ravindra Jadeja hit a six, then got his line wrong and Jadeja hit a four to pull off a stunning win.
"I was just trying to swing hard because every ball was important," Jadeja said of the dramatic last over.
"I knew anything could happen, so I was trying to swing hard and hit it straight."
Victory gave Chennai a record-equalling fifth title in front of a patient 75,000 crowd at Narendra Modi Stadium in Ahmedabad and gave retiring batter Ambati Rayudu a sixth IPL title, tying him with Rohit Sharma as the league's most successful players.
The league needed three days to play the decider. It was washed out on Sunday, started late Monday and finished in the early hours of Tuesday. But it was worth it.
Gujarat were made to bat first and posted 4-214 — the highest ever total in a final — highlighted by 96 from Sai Sudharsan.
Rain halted Chennai's chase in the first over for nearly two-and-a-half hours, and reduced the target to 171 in 15 overs. Chennai needed every single ball to reach it five down.
A fantastic launch was shared by Devon Conway (47 off 25 balls) and Ruturaj Gaikwad (26 off 16). They raised a half-century stand within the four-over powerplay, including 17 runs off legspinner Rashid Khan's first over.
Spinner Noor Ahmad removed both openers in the same over but Chennai kept coming hard. Ajinkya Rahane added 27 off 13, and Rayudu punished a loose Mohit Sharma with 6-4-6 before he was caught and bowled next ball.
Captain MS Dhoni also fell to Mohit Sharma, for a duck, leaving Shivam Dube (32 not out off 21) with Jadeja still needing 22 runs.
Mohammed Shami bowled a brilliant penultimate over to give Mohit Sharma a cushion of defending 13 in the final over. Mohit Sharma, who ended up with 3-36, conceded just three runs off the first four deliveries until Jadeja's (15no) last-gasp heroics.
Earlier, Chennai's early lapses in the field gave Gujarat momentum. Deepak Chahar missed catching chances against Shubman Gill and Wriddhiman Saha.
Gill, who top-scored in the tournament with 890 runs, made 39 off 20 before he stumped by Dhoni. Saha made 54.
Sudharsan shared two half-century stands; 64 with Saha and 81 off 33 balls with captain Hardik Pandya.
Sudharsan smashed eight boundaries and six maximums and dominated the death overs. He was in sight of a deserving century in the final over until pacer Matheesha Pathirana had him lbw with a superb yorker.
With Reuters.
