Opting to bat in this must-win game, Rajasthan Royals could only muster 158 for eight despite Jos Buttler's blazing 58-ball 82 at the SMS.
Despite a decent total on the board, Rajasthan staged a strong fightback with the ball as it restricted Kings XI Punjab to 143 for seven in the stipulated 20 overs.
Languishing at the bottom of the table prior to this game, RR have now moved to sixth place, while KXIP remained in third position.
RR reduced Kings to 19 for three in the fourth over and the visitors struggled to recover from the horrendous start, as they soon found themselves stuttering at 45 for four and then 66 for five, with eight overs left.
For Kings XI Punjab, Rahul played the lone ranger with 95 off 70 balls, his fourth half century of the ongoing league. KXIP needed 32 runs in the last over and Rahul's six and two fours were not enough.
The good start was provided by Krishnappa Gowtham as the off-spinner scalped dangerous Chris Gayle with the first ball of the third over. The spinner slid one down the leg side and Gayle charged down the wicket, only to be excellently stumped by Buttler.
The massive breakthrough spurred Royals and they soon had more reason to cheer as Gowtham removed KXIP skipper Ravichandran Ashwin, who promoted himself up the order, two balls later.
Jofra Archer then got into the act as he had Karun Nair hitting one high in the air for Jaidev Unadkat to complete a well-judged catch.
Wickets kept falling and runs were too hard to come by but Rahul held fort, mixing caution with aggression with his team in a crisis situation.
Ish Sodhi bowled beautifully to not only take a wicket - of Akshdeep Nath -- but also stymie the KXIP run rate. The New Zealand leg-spinner's turning deliveries and variations had the legendary Shane Warne applauding from the dugout.
Earlier, Buttler led the way with a 82-run knock before Kings XI Punjab bowlers fought back.
Pacer Andre Tye was the most successful KXIP bowler, returning figures of 4/34, while mystery spinner Mujeeb Ur Rahman picked up 2/21 in four overs.
Buttler began Royals' innings in earnest, hitting Marcus Stoinis for two successive boundaries in the first over.
Skipper Ajinkya Rahane was dismissed by Tye, who fooled the batsman with a knuckle ball, inducing an edge to extra cover. But Buttler continued his onslaught on the Rajasthan bowlers as he picked two consecutive boundaries off Tye.
Gowtham also departed quickly as he was sent back by Stoinis in the seventh over.
A half century partnership then ensued between Buttler and the talented Sanju Samson (22) but the run rate dropped as the Royals batsmen, including the Englishman, struggled to find the boundaries.
After the brisk start, there was a period in the middle overs when Rajasthan Royals failed to hit a boundary for 25 balls. Buttler finally managed a boundary off Mujeeb Ur Rahman and then got a four off the bowling of Axar, thanks to poor fielding by Tye.
But that was it as RR again went without a boundary for 14 deliveries before Samson produced a flat-batted six off Ravichandran Ashiwn, sending the ball over long-off.
Samson brought up the fifty partnership by playing Ashwin for another boundary, but Mujeeb struck for Kings XI Punjab when he had the batsman who struggled to play freely during his 18-ball stay in the middle.
Finally, Buttler's innings came to an end when Mujeeb had him stumped with Royals' score reading 132 for four in the 17th over. He stuck nine fours and a six.
Stuart Binny hit Tye for a six but Rajasthan simply lost their after a flying start.
(With inputs from agencies)