After Rajasthan captain Sanju Samson won the toss and elected to field, their bowling attack laid the foundation for the comprehensive victory by restricting Bangalore to 157-8.
Buttler, this season's leading IPL scorer, then smashed 106 not out off 60 balls as 2008 champions Rajasthan romped home with 11 balls to spare.
Sunday's final will be a rematch of Tuesday's first qualifier in which IPL debutants Gujarat beat Rajasthan by seven wickets.
Put in to bat, Bangalore could not really get going and crossed the 150-mark largely because of Rajat Patidar's breezy 58.
Bangalore's batting otherwise did not click against Rajasthan's disciplined bowling spearheaded by Prasidh Krishna and Obed McCoy, who claimed three wickets apiece.
Krishna dismissed Virat Kohli for seven in the second over and McCoy removed Bangalore captain Faf du Plessis (25) in the 11th to dent Bangalore's top order.
Glenn Maxwell could not capitalise on the start he got either and was dismissed by Trent Boult for 24.
Patidar smashed three sixes in his 42-ball cameo but Bangalore still fell well short of the 175-mark, which would have been a par score at the ground.
Rajasthan's chase got off to a rollicking start with Buttler maintaining his red-hot form and raising 61 runs in five overs with opening partner Yashasvi Jaiswal (21).
Buttler was on 66 when Dinesh Karthik dropped him in what proved a costly mistake.
Samson fell for 23 but Buttler could not be denied his fourth hundred this season and the Englishman sealed Rajasthan's victory with his sixth six.