The final flourish to the innings was provided by Pandya, who smashed a four and 3 sixes en-route to an unbeaten 11 ball 28 as Mumbai finished with 187/5 in their 20 overs.
When Buttler departed in the 14th over, Rajasthan needed 41 runs.
With the required run-rate over nine right from the offset, Buttler and Ajinkya Rahane put on 60 for the opening wicket.
South African De Kock was the wrecker-in-chief as he hammered six fours and four sixes in his 52-ball knock and got able support from skipper Rohit Sharma (47 off 32 balls), who made a comeback after missing out the last Mumbai game due to a leg injury.
Bowling has been some sort of concern for Mumbai especially the form of Hardik Pandya with the ball. If Rohit comes back in the playing eleven, it will further strengthen Mumbai's batting line-up, which features some dependable names like Hardik Pandya, Krunal Pandya, Quinton de Kock and Ishan Kishan.
On the eve of Mumbai Indians' match against Kings XI Punjab, Rohit Sharma seemed to pull his muscle and lay on the ground and looked in torment.
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A 28-run hand from Ben Stokes and a 7-ball 19 from Shreyas Gopal helped Rajasthan post a 151-run total on the board, which was at least 15 runs below the par score.
Needing 41 runs from 41 balls, Rajasthan slipped to 174-6, with England batsman Liam Livingstone making just one on his IPL debut. While the strike bowlers conceded runs, the side dropped crucial catches in the end to worsen things. Once he holed out to long off, the visitors threatened to collapse as they lost five wickets in the space of 17 runs, with Krunal Pandya taking three to bring MI back into the game.
Suryakumar Yadav, who replaced Rohit in the middle, looked in a mood to go big, as he moved to 16 off 9 balls, but Dhawal Kulkarni dismissed the right-hander as RR scalped two quick wickets. In the next two overs, the two scored 26 runs as the home team raced past fifty in the fifth over. Jofra Archer is menacing with the ball, as is Varun Aaron and Oshane Thomas.
Kieron Pollard, whose 31-ball 83-run blitz powered MI to a win against Kings XI Punjab in their previous game, failed to score big and got out for six as Archer struck for the second time.