Despite a slow innings, SRH accelerated towards the death, with strong finishing acts by Kane Williamson and Priyam Garg supplementing Manish Pandey's 54 and captain David Warner's measured 48.
RR's chase looked a lost cause from the outset as all three overseas batsmen - including the returning Ben Stokes - returned to the shed within the first five overs. Uthappa and Samson too failed to impress, furthering RR's slide.
Just when the equation looked out of control, Rahul Tewatia and young Riyan Parag took the attack to the opposition. With two needed off the last two, Parag struck a six to ensure RR that are still within reach of the top teams in this tournament.
Here are the player ratings from the SRH vs RR IPL 2020 game.
IPL 2020, SRH vs RR: RR Player Ratings
Ben Stokes: 4/10
On comeback from quarantine, Stokes loosened up with a solitary, tight over and was sent to open the innings. He struck a boundary, but was dismissed edging a pull back onto his stumps.
Jos Buttler: 4.5/10
Shouldering massive responsibility in this line-up, Buttler failed to deliver for RR. He got a start with 16 off 13, but edged one to the keeper to end his stay.
Steve Smith: 2.5/10
Smith had a good day as captain for the most part in the field. With bat in hand, he perished early going for an entirely unnecessary second run, leaving an inexperienced middle order with a lot to do.
Sanju Samson: 4.5/10
After the dismissal of the top three, Samson had to shoulder the weight of RR's expectations, which he seemed to be doing until his innings of 26 off 25 was ended by Rashid. He did take an excellent catch to dismiss Jonny Bairstow - it just so happened that Bairstow took the catch of Samson in return.
Robin Uthappa: 4/10
Uthappa looked comfortable at the crease for probably the first time this season. It was just a pity then that he was dismissed by Rashid and could not contribute more than 18 runs towards the team's cause.
Riyan Parag: 8/10
Riyan Parag was excellent for RR at the death with bat in hand. He showed fearlessness against the likes of Khaleel and Sandeep, and scored four boundaries in total, apart from the winning hit.
Rahul Tewatia: 8.5/10
Tewatia's star has only been rising this season for RR as his perfectly timed late assault turned the game. His three boundaries in a row against Rashid significantly dented SRH's plans. With ball in hand, he went wicketless but bowled reasonably.
Jaydev Unadkat: 6.5/10
Returning to the team on a pitch suited for his variations, Unadkat bowled as if to prove a point, delivering three economical overs with a wicket to go with them. His final over went for 16, although he still ended up with an economy rate below 8.
Jofra Archer: 8/10
Outstanding with ball in hand, Archer gave away just 25 runs in his four. His wicket of captain Warner was crucial, and also visually spectacular as he destroyed the southpaw's stumps.
Shreyas Gopal: 6/10
While Gopal was economical once again, he may have wanted a wicket against his name, particularly on a conducive pitch. The performance of Rashid demonstrated the turn on offer, which Gopal was unable to use to his advantage.
Kartik Tyagi: 5.5/10
Another slightly expensive outing for Tyagi, although he seems to be chalking up good pace. He did get the important wicket of Bairstow, but he did not complete his quota of overs.