Chasing 151 for a win, Kings XI lost dangerous Chris Gayle (16) in the fourth over with their scoreboard reading 18. Deepak Hooda took a brilliant catch at long-on boundary off Rashid Khan's (1/20) bowling to send the West Indian packing.
Rahul and Agarwal then complemented each other brilliantly as the duo mixed caution with aggression to literally take the game away from Sunrisers.
While Rahul was the enforcer, Agarwal matched his Karnataka teammate with his timing and on the rise shots that included a delectable boundary through covers and a lofted six over the long-off boundary.
Rahul reached his half-century off 34 balls with a boundary off Mohammad Nabi through the wide long-on region. On the other hand, Agarwal departed soon after reaching his fifty while going for a big shot, caught by Vijay Shankar at deep midwicket off Sandeep Sharma and four balls later Miller to was dismissed by the pacer as the left-hander went for an expansive shot.
Kings XI needed 16 runs off the last two overs and the pressure got the better of new man Mandeep Singh, caught by Hooda off Siddharth Kaul's brilliant penultimate over that yielded just five runs.
The pressure shifted to Kings XI in no time as they needed 11 runs off the last over off Nabi but Sam Curran (5 not out) and Rahul played sensibly without committing any harakiri to reach home with a ball to spare.
Earlier David Warner struck his fourth fifty of the season before Deepak Hooda played a cameo in the final over to lift Sunrisers to a challenging 150 for four against KXIP.
The orange army suffered an early blow in the form of Jonny Bairstow (1) after being sent into bat. The early dismissal, together with some disciplined bowling from Kings XI, made life difficult for Sunrisers batsmen as Warner and the new man in Vijay Shankar (26) found the going tough.
The duo failed to strike big and just when it was time to cut loose after a slow start, Shankar edged an Ashwin (1/30) delivery to K L Rahul behind the stumps as Sunrisers slumped to 56 for two after 10.4 overs.
Promoted up the order, Mohammad Nabi (12) fell victim to an unfortunate run out after adding just 24 runs with Warner.
Warner and Manish Pandey (19) then added 55 runs for the fourth wicket to take Sunrisers forward before Hooda finished off the innings in style to give Sunrisers' bowlers a total to defend.