Titans captain Pandya took 3-17, including the prize scalp of England's Jos Buttler for 39 to restrict Royals to 130-9 and then hit 34 from 30 balls.
Shubman Gill top-scored with 45 not out and the India batter hit the first ball of the 18th over for six to win the match in front of a record crowd of almost 105,000 people in Ahmedabad
The Titans triumph was built on a good draft: Mohammed Shami, Rashid Khan, Lockie Ferguson and Pandya combined to make up an excellent bowling attack, with batting power coming from Gill, David Miller and Matthew Wade.
But putting a group of talented players together does not automatically bring success, and Pandya has expertly led them from the front despite captaining in the IPL for the first time.
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In the final, on the biggest stage, he took the three prize wickets of Buttler, opposing captain Sanju Samson and Shimron Hetmyer and rotated his bowlers perfectly.
He was well supported by one of the world's best white-ball bowlers, Afghanistan's Rashid Khan, who took 1-18.
And when the batting stuttered at 23-2, he stopped any threat of a complete collapse by calmly negating Royals' bowling attack alongside Gill.
Although his side may not have secured the trophy, England's Buttler finishes as the winner of the Orange Cap, awarded to the highest run-scorer.
He hit four centuries in amassing 863 runs in 17 innings to put him second behind India superstar Virat Kohli's 973 on the list of most runs scored in a single IPL campaign.
While he was unable to replicate the fluency of his match-winning 106 not out that propelled his side into this final, his reputation as one of the world's most destructive T20 batters has grown considerably.
Rajasthan leg-spinner Yuzvendra Chahal also finishes with the purple cap, awarded to the leading wicket-taker - a poignant tribute to the late great Shane Warne, who led the Royals to the IPL title in its first edition in 2008.
No one can say when sports began. Since it is impossible to imagine a time when children did not spontaneously run races or wrestle, it is clear that children have always included sports in their play, but one can only speculate about the emergence of sports as autotelic physical contests for adults. Hunters are depicted in prehistoric art, but it cannot be known whether the hunters pursued their prey in a mood of grim necessity or with the joyful abandon of sportsmen.
It is certain, however, from the rich literary and iconographic evidence of all ancient civilizations that hunting soon became an end in itself—at least for royalty and nobility. Archaeological evidence also indicates that ball games were common among ancient peoples as different as the Chinese and the Aztecs. If ball games were contests rather than noncompetitive ritual performances, such as the Japanese football game kemari, then they were sports in the most rigorously defined sense. That it cannot simply be assumed that they were contests is clear from the evidence presented by Greek and Roman antiquity, which indicates that ball games had been for the most part playful pastimes like those recommended for health by the Greek physician Galen in the 2nd century ce.