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Along with Riyan Parag (42 not out off 26 balls), Tewatia won the game in 'Royals' style keeping Steve Smith's men in the mix after RR was reduced to 78 for 5 in 12 overs.
With two needed off two balls, Parag hit Khaleel Ahmed for a six over extra cover and broke into an impromptu 'Bihu jig'. They added 85 runs for the sixth wicket in eight overs when their illustrious international stars flattered to deceive.
Tewatia brought back memories of the Sharjah night but this time it was Rashid Khan who was at receiving end in the 18th over as the left-hander struck three consecutive boundaries.
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With 22 needed off two overs, Tewatia launched into T Natarajan, who lost his length trying to bowl yorkers, for a four and a six over short fine leg that swung the match in favour of Royals.
The bizarre decision to send comeback man Ben Stokes (5) up the order didn't work too well as the slowness of the track did him in. Left-arm pacer Khaleel got one to rear up outside the off-stump but the ball came late as Stokes, shaping for a pull, played it onto his stumps.
Steve Smith (5) chanced Vijay Shankar's arm in the deep but failed in the process while Jos Buttler (16) got a delivery from Khaleel that came in after the fingers were rolled over. The inside edge was taken by a diving Jonny Bairstow as Royals were reduced to 26 for 3 inside Powerplay.
Earlier, Manish Pandey struck an impressive half-century but Rajasthan Royals restricted Sunrisers Hyderabad to 158 for 4 in stipulated overs.
With the pitches getting slower by the day and stroke-making becoming increasingly difficult, Pandey struggled initially but finished with two fours and three sixes in his 54 off 44 balls.
He had a partnership of 73 off 10 overs for the second wicket with skipper David Warner (48 off 38 balls), who also looked scratchy and struggled for timing.
Kane Williamson (22 not out off 12 balls) showed his class briefly at the end, including a one-handed straight six off Royals' best bowler Jofra Archer (1/25 in 4 overs) and ended with another off the last delivery of the penultimate over.
The young Priyam Garg (15 off 8 balls) also made a valuable little contribution in the final few overs of the innings.
It was one of the better days for Jaydev Unadkat (1/31 in 4 overs) as his variation of slower deliveries caused some trouble for the batsmen with only 26 runs coming off the Powerplay.
In all, Rajasthan bowlers managed 42 dot balls, which is seven overs without a run being scored.
Bairstow (16 off 19 balls) and Warner failed to get the ball off square and the harder they hit, the lesser distance it traversed.
Finally, Bairstow broke the shackles with a six off Kartik Tyagi but off the very next delivery, he was taken brilliantly in the deep by Sanju Samson.
Pandey and Warner then steadied the ship hitting the occasional sixes. Pandey's straight six off Shreyas Gopal's tossed up delivery was a magnificent shot.
In fact, the Sunrisers batsmen found it easier to hit sixes -- nine of them in all than the fours (only six) during their innings.
SRH made one change in its playing 11 bringing in Vijay Shankar in place of Abdul Samad. Meanwhile, Rajasthan made three changes.
SRH playing 11: David Warner(c), Jonny Bairstow(w), Manish Pandey, Kane Williamson,
, Priyam Garg, Abhishek Sharma, Rashid Khan, Sandeep Sharma, Khaleel Ahmed, T Natarajan.