Trent Boult had given Rajasthan an early breakthrough when he had Wriddhiman Saha caught behind off a superb second ball which nipped away from the right-hander and got a faint edge.
But Shubman Gill and Matthew Wade both played significant cameos of 35 runs each before Miller and Pandya led the way for Gujarat, which had topped the league stage with 10 wins.
Obed McCoy raised Rajasthan’s hopes when the left-arm West Indian fast bowler gave away only seven runs in the penultimate over, in which Miller raised his fifty off 34 balls with a single.
But Miller kept his nerves and smacked Krishna’s first ball over long-on before hitting the fast bowler for two big sixes over midwicket and cruised his team to a dream IPL final in its debut season.
Earlier, Buttler’s astonishing run of form continued as the Englishman raised his tally of runs to 718 with three centuries and four solid half centuries from 15 games.
Luck also favored Buttler as he escaped three dropped catches in an innings which featured a dozen boundaries and two late sixes.
Captain Sanju Samson played well for his 47 off 26 balls before dragging a catch at long-on midway through the innings. Devdutt Paddikal (28) scored freely against the spinners but was tied down by the Gujarat fast bowlers before he played onto Pandya in the 15th over.
But Buttler counter-attacked in the death overs and raised his half century off 42 balls. The Englishman hit eight fours and two sixes in the last four overs that also included four boundaries in fast bowler Yash Dayal’s one over and three off Joseph Alzarri’s penultimate over.
Buttler was run out in the last over while going for the second run, but his superlative effort was upstaged by Miller and Pandya’s brilliant run-chase.
Hardik Pandya, who scored an unbeaten 40, credited family for his success.
“I have tried to balance things. Have had difficult times, certain situations, my body, and bubble life. But my son, wife, and brother have played a big role. Allowed me to be neutral.”