Sam Curran took over as captain with Shikhar Dhawan battling a niggle but found no luck at the toss with Sanju Samson opting to chase.
PBKS got off to a sedate start with only 38 coming in the PowerPlay for the loss of Atharva Taide.
Yuzvendra Chahal struck in his first over to dismiss Prabhsimran Singh.
Keshav Maharaj took 2 for 23 from his 4 overs. This included the wickets of Bairstow and Curran.
Rajasthan Royals had an interesting day in the field. While Jurel took three outfield catches, Samson was involved in two moments where he and another fielder went for the same high ball.
Ashutosh Sharma scored a quickfire 31 to give PBKS a somewhat competitive score of 147.
Yashasvi Jaiswal Rajasthan Royals off to a good start in the chase with a 28-ball 38.
Kagiso Rabada dragged PBKS back into the game with the wickets of Jaiswal and Samson.
Sam Curran added two wickets of his own and RR were left having to score 34 from the final 3 overs.
Shimron Hetmyer scored 27* off 10 to take RR home with a balls to spare.