Chasing 224 for victory, Rajasthan looked in trouble at 121-6 in the 13th over but Buttler moved through the gears in his 60-ball blitz to achieve the target with two wickets to spare at Kolkata's Eden Gardens.
Rajasthan equalled their own record from 2020 when they chased down 224 against Kings XI Punjab in Sharjah.
Buttler, who came in as an impact substitute, reached his second ton of the season in 55 balls with a six off Varun Chakravarthy at the start of the last over.
Buttler, struggling with cramp, then played out three dot balls before a two and a single on the final delivery ensured Rajasthan held on to top spot in the table with six wins in seven matches.
England's Buttler, who hit nine fours and six sixes, moved ahead of Chris Gayle with seven IPL tons and is only behind Virat Kohli's eight in the T20 tournament.
Buttler built key partnerships including 50 runs with Riyan Parag (34), 57 with Rovman Powell (26) and then an unbeaten 38-run stand with Avesh Khan (0 not out).
Spinners Narine, Chakravarthy and fast bowler Harshit Rana took two wickets each for KKR.
Narine hammered 109 off 56 balls to guide Kolkata, who stay second in the 10-team standings, to 223-6.
Narine put on 85 runs for the second wicket with Angkrish Raghuvanshi, who hit 30, and got together for a 51-run stand with Andre Russell.
Narine, playing his 504th T20 match, reached his ton from 49 balls with a six and a four off Yuzvendra Chahal for Kolkata's third hundred in the IPL as he jumped for joy.
He was finally bowled by a Trent Boult yorker before he returned to a standing ovation.
Narine moved into the top three in the batting charts led by Royal Challengers Benguluru's Kohli (361) with 276 runs.
Rinku Singh finished off the innings on a high with his unbeaten nine-ball 20 including a four and two sixes.
