Mohammad Shami was expensive but came good in the final overs, scalping two wickets.
After this win, KXIP Punjab grabbed the fourth spot in the points table with 10 points to keep play-off hopes alive.
However, it was Rajasthan’s sixth loss and they will need to pull up their socks if they have to salvage any hopes of making it to the knockout stage.
Rahul, who was named in the World Cup squad on Monday, recovered after a slow start to post a 47-ball 52 studded with three fours and two sixes. He was ably supported by David Miller (40 off 27) as the duo shared a 85-run stand to lay the foundation.
Pacer Jofra Archer (3/15) returned with an exceptional three-wicket haul to emerge as the best bowler for the Royals.
Chris Gayle (30) smashed Jaydev Unadkat for a couple of sixes in the second over, before blasting Dhawal Kulkarni for a four and a six in the fifth over.
Archer then had him caught behind by Sanju Samson in the sixth over as KXIP were 39 for one in the first powerplay overs.
Playing his first IPL game this season, New Zealand’s Ish Sodhi was then introduced into the attack and Mayank Agarwal (26 off 12) clobbered him for a six in the fourth ball.
Agarwal then picked up a four and a six off Shreyas Gopal before Sodhi returned to remove him. Trying to play a slog sweep, Agarwal was caught by Archer at long-on.
Left stranded on the other end, Rahul tried to steady the ship with Miller, who came into the side due to the last-minute ankle injury of Moises Henriques.
The duo took singles and twos before Rahul finally scored his first boundary when he lifted a Unadkat delivery across the mid-off region.
In the 14th over, Rahul and Miller exploded after bringing up the hundred for KXIP. The duo amassed 19 runs off Sodhi’s over, his last, with Rahul smoking a massive six over deep square leg and Miller thumping one over long-off.
The two batsmen piled up 20 runs in the next over with Rahul hitting an inside-out shot over cover for a six and a four off Unadkat, and Miller disposing a full-toss over deep midwicket.
Gopal then bowled an economical over next to compete his quota of four overs.
In the next over, Archer dismissed Miller on a no-ball before Rahul sent one across the mid-off area to complete his fifty in 45 balls.
Rahul perished early in the 18th over off Unadkat and Archer then bowled a superb over, removing Nicholas Pooran (5) and Mandeep Singh (0). Miller too was sent packing early in the 20th over by Kulkarni.
Ashwin then smashed a four and successive sixes in the last two balls to put KXIP in a strong position.
(With PTI inputs)