Opening the innings, Buttler smashed a breathtaking 124 off 64 balls while Sanju Samson was effective in his 48 off 33 deliveries which powered Rajasthan to a commanding 220 for three.
Even a change in captaincy couldn''t bring in luck for SRH as they could manage only 165 for eight in their 20 overs.
Chris Morris (3/29) and Mustafizur Rahman (3/20) did the bulk of the work with the ball while Kartik Tyagi (1/32) Rahul Twetia (1/45) picked a wicket apiece.
With the win, the Royals moved up to fifth spot while SRH continued to stay at the bottom, having won only one match all season.
Looking to register their second win of the season, SRH raced to 57 for no loss in the first six overs.
However, Bangladesh pacer Rahman struck right after the first strategic time out, getting rid of Manish Pandey (31). The dangerous Jonny Bairstow (30) and Vijay Shankar (8) soon followed.
With the pressure mounting, skipper Kane Williamson (20) went for the big shot only to be caught at deep midwicket by Morris off Tyagi as wickets tumbled at regular intervals.
Mohammad Nabi (17 off 5) injected some hope in the SRH camp, as he smashed Tewatia for two sixes in the 14th over. However, the Afghan was back in the dug out after a quick cameo.
With 91 needed in the last five overs the lower and middle order struggled.
In the end the, top heavy SRH did not have enough fire-power to pull off the mammoth chase.
Earlier, put in to bat, Buttler and Samson stitched a 150-run partnership for the second wicket after the Royals lost opener Yashasvi Jaiswal (12) cheaply.
While the Englishman hit the ball 11 fours apart from eight maximums, Samson also had four fours and two sixes to his credit.
For SRH, Rashid Khan (1/24), Vijay Shankar (1/42) and Sandeep Sharma (1/50) picked a wicket each.
Put into bat, the Royals were off to a sedate start as they managed just five runs of the first two overs.
Williamson, searching for wickets early on in the innings, introduced spin in third over by bringing in star bowler Rashid.
Jaiswal smashed three fours, before the Afghan showed his class and trapped the youngster leg before.
RR skipper Samson, who was dropped on 23 by Manish Pandey in the 10th over, announced his arrival with a six over mid-wicket off pacer Khaleel Ahmed.
At the other end, Buttler, who looked in sublime touch, also hit Bhuvneshwar Kumar for two boundaries in the sixth over as the Royals amassed 42 runs for the loss of one wicket in the Powerplay.
The duo continued to hit boundaries at regular intervals at the small Feroz Shah Kotla ground, collecting 18 runs, which included two sixes, off all-rounder Vijay Shankar in the seventh over.
Having successfully navigated Rashid’s four overs, Buttler and Samson upped the ante in the 13th over, plundering 17 runs.The Englishman muscled a six over wide long on before lofting one over extra-cover for boundary.
With all bowlers leaking runs, Williamson turned to Mohammad Nabi, who is playing his second game of the season, but Buttler hammered the off-spinner for two sixes and as many fours.
Vijay Shankar managed to get rid of Samson in the 17th over with young Riyan Parag (15 not out) walking in.
There was no stopping Buttler, who was in complete control, as he continued to hit boundaries at will. Sandeep Sharma, eventually brought his innings to an end of the penultimate over but he had inflicted the required damage by then.
SRH were guilty of being sloppy in the field, dropping catches and missing run outs.