But still RR got two points to stay afloat with Jaiswal (50 off 36) scripting the chase, adding 73 off 49 balls with Padikkal (51 off 30) and another 47 off 22 balls with Shimron Hetmyer (46) as RR romped home in 19.4 overs.
With the win, RR moved to fifth spot with 14 points, same as RCB (4th) and Mumbai Indians (6th), who both still have a match to play in the league stage.
The loss meant, PBKS are officially out of the IPL.
Chasing 188, RR suffered an early setback with Kagiso Rabada getting Jos Buttler LBW for his third duck.
But Padikkal and Jaiswal batted with purpose to take RR to 85 for 1 in 9.4 overs.
While Jaiswal began the chase with a hat-trick of fours, Padikkal, who was promoted up the order, then took the charge, sending the bowlers on a leather hunt.
But RR lost Padikkal and skipper Sanju Samson (3) in quick succession to leave them at 90 for 3 in the 11th over.
Jaiswal then found a perfect partner in Hetmyer, who slipped into the role of the aggressor with three sixes early on.
Jaiswal completed his fifty in 35 balls before falling to a reverse hit off Nathan Ellis.
With both Jaiswal and Padikkal departing after completing their fifties, RR still needed 51 off 33 balls and it was Riyan Parag (20 off 12 balls) who slammed two successive sixes off Rabada to bring the equation down.
But PBKS skipper Shikhar Dhawan pulled off a sensational catch to end Hetymer’s stay even as RR brought in Dhruv Jurel as an impact sub, who clobbered a six in the fourth ball of the last over to knock off the winning runs.
Earlier, PBKS were down 50 for 4 in 6.3 overs but Curran and Jitesh added 64 to resurrect the innings with the latter being the aggressor.
Curran and Shahrukh then piled up 73 off 37 balls with 46 of them coming off the last 2 overs to take them to a good score.
It was the second last over which proved to be a turning point with Yuzvendra Chahal, who had conceded 12 runs in his first three overs, went for 28 runs with Curran and Shahrukh producing some clinical hitting.
Shahrukh then milked Trent Boult (1/35) for 18 runs as the last five overs yielded 70 runs.
Forced into the XI due to R Ashwin’s back spasm, Adam Zampa finished with 1 for 26, while Navdeep (3/40) picked up three wickets but Sandeep Sharma had a forgettable outing as he bled 46.
Boult pegged PBKS back early on, dismissing Prabhsimran Singh (2) with a caught and bowl effort but Dhawan (17) and Atharva Taide (19) picked some boundaries as they were 38 for 1 in 3.3 overs.
However, playing only his second game, Navdeep broke the partnership with Atharva (19) holing out at midwicket after hitting successive fours.
Boult and Zampa conceded just 3 runs each in the next two overs which put Dhawan under pressure and he was then trapped by Zampa in front.
Liam Livingstone was Saini’s second victim as PBKS slipped to 50 for 4.
However, after the strategic timeout, Jitesh changed gears, smashing Sandeep Sharma for two maximums before thumping Zampa across the deep extra cover.
Saini was next in his firing line, slicing one across point before smoking him over deep extra cover. A short ball was next hammered across the mid-wicket region. However, a slower delivery did the trick with Jitesh holing out at extra cover.
Shahrukh then joined Curran but they couldn’t find the big hits initially before exploding in the 19th over bowled by Chahal.................................
The first two balls were sent for a four and six by Shahrukh before Curran took over, clobbering two sixes and a four to take PBKS across the 150-mark. Shahrukh then blasted a six and four to finish it in style.