The win helped RR to the fifth spot on the table, from the seventh spot, with 12 points while KXIP, despite being at the receiving end, remains at the fourth place with 12 points. RR are also level on points with Kolkata Knight Riders who they replaced at sixth place.
Mumbai, who have already qualified for the playoffs, and Bangalore hold the top two slots in the table respectively.
Chasing a decent 186-run target, Ben Stokes (50) and Robin Uthappa (30) handed an ideal start to their side, adding 54 runs in the initial five overs with the former scoring in bulk.
Ten runs later, Chris Jordan (1/44) came with the first break, dismissing Stokes in the sixth over when he had just completed his half-century.
Sanju Samson (48) and Uthappa then added 51 runs for the second wicket as RR crossed the three-digit mark in 9.3 overs.
Murugan Ashwin (1/43) got the better of Uthappa in the 11th over which saw RR at 111/2.
RR skipper Steve Smith (31 not out off 20) then gave company to Samson for a brief 34-run stand before a run-out saw the latter walking back to the dugout in the 15th over.
With some fireworks in the middle, Smith and Jos Buttler (unbeaten 22 off 11) then took the Punjab bowlers to cleaners as the pair amassed 41 runs off just 19 balls to help RR cross the line with 15 balls and seven wickets to spare.
For KXIP, M Ashwin and Jordan managed a wicket apiece while the others remained wicketless.
Earlier, Gayle's blistering 99 and KL Rahul's scintillating 46 took KXIP to 185/4 in the allotted 20 overs.
Asked to bat, Punjab was jolted early as Jofra Archer (2/26) struck in the very first over to send back opener Mandeep Singh for a duck.
Rahul and Gayle then took control of the proceedings, forging a crucial 120-run stand for the second wicket.
With all the Royals bowler struggling, Ben Stokes (2/32) came with a major relief when he dismissed the Punjab skipper, who missed his half-century merely by four runs, in the 15th over.
Nicholas Pooran (22) and Gayle were then involved in a 41-run stand as KXIP crossed the 150-run mark.
Stokes then accounted for the wicket of Pooran, leaving KXIP at 162/3 in 18 overs.
While trying to escalate the run-rate, Gayle tried to go big against Archer in the last over but the England bowler had the last laugh as he castled Gayle, who missed a well-deserved ton by a run. Gayle's knock was laced with six boundaries and eight huge sixes.
During his knock, Gayle became the first batsman to get to 1,000 sixes in T20 cricket history when he smashed the seventh of his eight sixes.
"Oh, 1,000 sixes! I do not know the record [of 1,000 sixes]. Still have to be hitting it well at the age of 41. Got to give thanks for that," said Gayle when told about his milestone.
Brief scores: Rajasthan Royals 186/3 wkts in 17.3 overs (Ben Stokes 50, Sanju Samson 48; Murugan Ashwin 1/43) beat Kings XI Punjab 185/4 wkts in 20 overs (Chris Gayle 99, KL Rahul 46; Jofra Archer 2/26) by 7 wickets