RR fell one run short while chasing KKR's target of 207.
The hosts looked in cruise control for most of the match, but a whirlwind knock of 45-ball 95 by RR's stand-in skipper Riyan Parag gave them hope of victory in the massive chase of 207.
Shubham Dubey (25* off 14) nearly pulled off 22 runs in the final over against Vaibhav Arora, but a run out on the last delivery saw KKR scrape a narrow win.
After the game, Parag took the blame on himself for RR’s loss, saying that his plan was to stay till the end and he made a miscalculation.
"I was just sad, about me getting out. I was planning to stay till the last over. We couldn't get much in the 16th and 17th, a miscalculation from my side. Should have finished it," Parag said at the post-match presentation.
"I think we could have found better options in the first six overs. The spinners did really well. We could have looked to cut down some runs with the ball. But the game was in our hands, we should have finished this," he added.
Earlier, the defending champions racked up 206/4 on the board after opting to bat first, courtesy of Andre Russell’s brutal 57* off 25 balls and vital contributions from Angkrish Raghuvanshi (44 off 31), Rahman
"I didn't want the bowlers to bowl back to back. Madhwal, was only playing his 2nd game. Now it sounds like we could have done something else but maybe the right decision, I don't know. Very difficult, he (Andre Russell) came in and took his time and then accelerated well. It was great to watch,” Parag remarked.
"It is a ground where sixes are hit, I knew the odd ball stopping and turning but I knew I had to pick my battles. I feel awful to give this interview here, but it is just how the game is. You have to be clinical, the consequences are here," he concluded.
The win kept KKR's playoff hopes alive while the Royals are already out of the reckoning.