The Indians put their opponents in to bat first but no doubt soon regretted that decision as opener Buttler plundered 100 off 68 balls.
Buttler had 26 runs in a dizzying fourth over alone and later put on 82 with captain Sanju Samson (30) for the third wicket in the biggest partnership of the match
One of the great limited-overs batsmen, Buttler's tally of a single hundred in 66 prior IPL matches was on the light side.
He was well on the way to his second century within four overs, though, with 38 runs off 20 balls at that stage.
Although that pace then slowed a little, it still required an elite bowler to eventually get Buttler, with a Jasprit Bumrah beauty among three wickets in the 19th over as he finished with 3-17.
Jos Buttler's second Indian Premier League century helped maintain Rajasthan Royals' winning start in 2022, setting the stage for a 23-run defeat of Mumbai Indians on Saturday (April 2).
Unfortunately for the Indians, already slightly behind in the game, their next boundary did not follow for almost three overs – during which time Chahal took his two wickets.