The Knight Riders were chasing 165 for victory, but a top-class opening burst by seamer Amit Singh and left-arm spinner Ankeet Chavan saw them lose three wickets off three balls.
At eight for three in the third over, Kolkata were looking like fish out of water and, despite a classy, defiant half-century from Manoj Tiwary and a late onslaught from Brett Lee, the victory was a most comfortable one for the Royals.
Jacques Kallis (5) was the first to fall, driving a slower ball from Amit straight to deep mid-off. The 30-year-old followed up the wicket of South Africa’s greatest batsman by having Indian star Gautam Gambhir caught behind for a duck off the next delivery.
Brendon McCullum (2) then seemed oblivious to the crisis as he walked across his stumps to the first ball of the next over and was trapped lbw by Chavan.
The Rajasthan team needed to use just five bowlers as the Knight Riders continued to lose wickets at regular intervals.
Yusuf Pathan briefly threatened as he scored 15, but the big-hitting Gujarati is frustratingly inconsistent and he skied Siddharth Trivedi to midwicket to leave Kolkata on 66 for five in the 11th over.
Lee is a dangerous striker of the ball and he hammered a pair of fours and sixes in his 25 off 11 balls before being bowled by a good slower ball from Kevon Cooper.
Tiwary finished with 59 off 49 balls, with seven fours, but it was not enough to prevent the Knight Riders from being bowled out in the final over.
Chavan took 2-23 and Amit 2-30 to set the early tone, while Trivedi claimed 2-25 to undermine the middle-order.
Cooper then grabbed 3-28 to earn himself the Purple Cap for the leading wicket-taker, while South African Johan Botha eventually bowled Tiwary to end the innings and finish with 1-34.
Brad Hodge and Ashok Menaria were the inspiration earlier with the bat as the Rajasthan Royals posted 164 for five.
Rajasthan had been sent in to bat and were hampered by both their openers being run out as they reached 62 for three after nine overs, before Menaria scored 40 off 30 balls and Hodge 44 off 29 deliveries as they shared a fourth-wicket stand of 64 in 7.3 overs.
Ajinkya Rahane, the hero of Rajasthan’s comprehensive opening win over the Punjab Kings XI, surrendered his wicket in the second over when he was run out by Gambhir for a duck, before Rahul Dravid and Shreevats Goswami added 43 for the second wicket in five overs.
Their stand was ended, however, by Dravid’s run out, by Iqbal Abdulla, for 26 and Rajat Bhatia, their most economical bowler, then struck a major blow for the Knight Riders as he bowled Goswami for 23.
Menaria and Hodge owned the middle overs, however, giving the Royals a competitive total in the process.
Hodge was content to set off at his own pace, scoring at a run-a-ball for his first 13 deliveries, before getting stuck into off-spinner Pathan in the 14th over.
The Australian cooked up two sixes and a four in the over of pies and the run-rate continued to rise as he smashed Kallis for successive boundaries in the next over.
Hodge eventually fell trying to scoop compatriot Lee and being caught behind, but Englishman Owais Shah immediately got down to business, facing two balls before hitting two fours and a six off his next four deliveries.
Lee bowled Menaria in an eventful penultimate over that also included a six and a four by Shah, as well as a no-ball that just cost two more runs off the free hit by the Western Cape Cobras batsman.
The Kolkata bowlers stuck to their game plans well, with Lee taking 2-29 and spinners Sunil Narine, the IPL rookie from the West Indies, (4-0-29-0) and Bhatia (4-0-27-1) systematically stifling the batsmen.