David Warner was forced to demote himself in the batting order courtesy of Kane Williamson's injury.
The Kiwi was promoted to open the innings and have a dash in the Powerplay as he wouldn't have been able to run freely and pick the singles later in the middle overs.
Williamson hit a quick 29 from 19 balls as he laid the foundation by adding 58 runs for the opening wicket with Jonny Bairstow (36).
Sunrisers lost wickets at regular intervals in the middle overs and lost the initiative.
Warner, who came in at No 4, was faced with the rebuilding task and played against his natural mode of dominating the bowlers.
Vijay Shankar threw his wicket away with a rash shot, but Warner found some hope in the young Jammu and Kashmir all-rounder Abdul Samad, who stroked 23 from 15 balls.
After mostly dealing in singles for most part of his innings, the real Warner only came to the fore in the final over bowled by Andre Russell, with Sunrisers needing 18 runs for victory.
He got on strike for the second ball, and flicked Russell past short fine leg for a four. He then lofted the next back over the bowler's head for another boundary.
The Australian left-hander made it three fours in a row when he clipped Russell for another boundary through square leg to take Sunrisers on the brink, with four needed from two balls for victory.
He then went for the heave over midwicket but got it off the inside half of the bat for two runs.
With two needed for victory off the final ball, Warner missed the flick and was hit on the pads but managed to collect a leg bye which tied the match and force it into the Super Over!
Warner single-handedly scripted the turnaround with an unbeaten 47 from 33 balls and somehow forced the game into the Super Over, which gave his team another shot at victory despite being so behind in the race at one point.
However, it was a case of so close yet so far for Sunrisers despite Warner's brilliance as they flopped with the bat in the Super Over, with Lockie Ferguson sending them crashing for two runs, and KKR winning easily.