Gujarat are now two points clear of second-placed Kolkata Knight Riders, while Rajasthan slipped to third.
Rajasthan made a great start to their chase as opener Jos Buttler unleashed an array of shots during his 54-run blitz off just 24 balls.
But Lockie Ferguson (3-23) ended Buttler's knock with a searing yorker, and David Miller took a stunning catch to dismiss Ravichandran Ashwin (eight).
Buttler hit eight fours and three sixes during his entertaining innings, peppered with some stunning scoop shots.
Royals captain Sanju Samson said losing quick wickets cost his team.
"If we would have had wickets in hand, this was chaseable.... We had the power and potential," he said.
Earlier, Gujarat made a shaky start, losing Matthew Wade, Vijay Shankar and Shubman Gill inside seven overs.
Wade was run out by Rassie van der Dussen, who made no mistake in hitting the stumps at the striker's end as the batters tried to steal a single.
Shankar edged a short and wide ball from Kuldeep Sen to be caught behind by Samson, while Gill fell to Riyan Parag.
Pandya went after the bowling attack, hitting Sen for three successive fours before smashing a six off Parag.
He raced to his half-century in just 33 deliveries before hammering off-spinner Ashwin for successive sixes.
Abhinav Manohar also played an attacking innings, hitting four fours and two sixes in his 43.
Titans skipper Pandya shared 86 for the fourth wicket with Manohar, and Miller scored a fine 31 not out off 14 balls to ensure a big total on the board.