The Knight Riders, chasing 169 to win, managed just 135 for five in their stipulated quota of overs.
The Shah Rukh [ Images ] Khan-owned team struggled to assert their authority on a slow-paced wicket and paid the price for leaving too much for too late.
It was the first win in this edition for the team from Rajasthan and came after successive defeats in their first three matches.
As regards the Knight Riders, it wwas their second straight defeat - after the loss against Chennai Super Kings [ Images ] at Kolkata on Tuesday - after they had started the campaign with a win in their opening two games.
Yusuf Pathan [ Images ], who had failed to make an impact with the bat, delivered with the ball on this occasion.
His four parsimonious overs cost Rajasthan just 23 runs while fetching them two vital wickets.
Captain Shane Warne [ Images ] may have failed to take a wicket but gave away just 27 runs off his four and asked the Kolkata batsmen a few questions.
Yusuf struck in the third over to peg the Knight Riders back and ensure Rajasthan an early wicket.
Manoj Tiwary (11) tried to manufacture a non-existent cut shot and saw his stumps get rattled in the process.
Cheteshwar Pujara [ Images ] (29) survived a run out in the first ball of the fourth over.
However, the youngster then eased pressure a bit with a couple of boundaries off Shaun Tait [ Images ], the first to square-leg and the next to backward point.
Munaf Patel [ Images ] was introduced into the attack in the fifth over and Pujatra greeted him with a couple off boundaries.
The batsman was fortunate to be dropped by Jhunjhunwala (off Trivedi) when he was on 24 (in the ninth over).
A steady 50-run partnership for the second wicket between Brad Hodge [ Images ] (36) and Pujara kept Kolkata Knight Riders in the hunt.
But just as the duo looked to threaten Trivedi finally had his man, castling Pujara in his third over.
In came captain Sourav Ganguly [ Images ] but despite their best efforts both he and Hodge struggled to break free against a resolute Rajasthan bowling, the duo getting increasingly frustrated in the process.
Yusuf sensed Hodge's frustration and took ample advantage of that, rattling his stumps and ensuring his side their third wicket.
After 15 overs, Kolkata had made just 99 for three, way behind the Rajasthan aggregate (124 for four) at that stage.
Moreover, their innings was yet to witness a shot getting the maximum benefit.
That eventually came from Shah's blade in the 17th over, when the batsman smashed a Munaf delivery over the long-on fence.
Shah doubled the tally in the next over, smashing Trivedi over midwicket for another maximum.
Sourav Ganguly made a 29-ball 33 before being dismissed in the final over, caught by Voges at deep midwicket.
It was one the worst Ganguly innings ever.
The former Indian captain, who has struggled to play his natural game in this format, witnessed his weakness against the short ball lay exposed yet again.
Ganguly, criticised by many for not contributing enough with the blade, in his effort to answer back scored a few but there was no authority in the manner in which he scored them.
Earlier, the team from Kolkata kept taking wickets at regular intervals to restrict the home side to a modest total.
In their stipulated 20 overs, Rajasthan managed 168 for eight, with debutant Adam Voges (37) using the long handle to good effect towards the end.
Voges' 22-ball knock was inclusive of two hits to the fence and two over it.
However, it was a total lesser than what their captain had envisaged at the toss.
Murali Kartik [ Images ] bolstered his reputation as the tournament's most economical bowler thus far, giving away just 25 runs off his four overs.
Dinda struck with the first ball, trapping Micheal Lumb plumb in front to ensure a perfect start for the Kolkata team.
Debutant Faiz Fazal survived a loud leg before appeal in the second ball, the first that he faced before hitting the final ball of the over to the mid-on boundary.
And in Dinda's second over, Fazal cut loose, hitting as many as three boundaries, including two off the first two balls.
The batsman displayed tremendous potential in his 23-ball 31, a knock inclusive of six hits to the fence.
But the introduction of Shane Bond in the fifth over earned Kolkata his wicket, as the paceman had him caught by Cheteshwar Pujara at mid-on.
However, Naman Ojha [ Images ] (27) eased the pressure to a considerable extent by slamming three boundaries in the next over bowled by Mathews.
After six overs, before the field restrictions ceased to exist, Rajasthan, despite having lost a couple of wickets, were in a comfortable position at 56 for two.
Ojha was unfortunately run out in the ninth over and that marked the arrival of Yusuf Pathan (15).
Yusuf, the memories of that magnificent 37-ball 100 against Mumbai Indians [ Images ] still afresh, began with a couple of boundaries in Bond's second over.
But he was done in by Dinda's change in pace soon after, hitting straight to Brad Hodge at deep square leg.
Abhishek Jhunjhunwala' 36-ball 45 was a perfect follow-up to his unbeaten 53 against Delhi Daredevils [ Images ] and gave the required consolidation to the Rajasthan innings.
However, he gave his wicket away when his team could ill-afford it. In the 18th over, Jhunjhunwala hit Ishant straight to Ganguly at midwicket and that ensured a procession of wickets.
Two balls later, Paras Dogra (0) edged to Saha behind the stumps. And Bond returned to account for Warne (1), caught by Manoj Tiwary at long-off, in his final over.
That the Rajasthan batsmen had failed to assert themselves in the match can be judged from the fact that the only two sixes in the innings came in Ishant's final over, both of the blade of Voges.
Earlier, Rajasthan won the toss and and their captain Shane Warne had no hesitation in opting to bat first.
"The wicket will get slower as the day progresses," reasoned Warne, adding, "It's 175-plus wicket and a good start is crucial for us."
Warne's opposite number Sourav Ganguly concurred.
"I would have batted first too. But the wicket looks damp and hopefully we will utilise this," said Ganguly.
KKR opted not to play Chris Gayle [ Images ] as he was reportedly down with fever.
Rajasthan Royals: Shane Warne (captain), Naman Ojha, Michael Lumb, Faiz Fazal, Abhishek Jhunjhunwala, Paras Dogra, Yusuf Pathan, Shaun Tait, Munaf Patel, Adam Voges, Siddharth Trivedi [ Images ].
Kolkata Knight Riders: Sourav Ganguly (captain), Brad Hodge, Owais Shah [ Images ], Cheteshwar Pujara, Manoj Tiwary, W Saha, Angelo Mathews [ Images ], Murali Kartik, Shane Bond, Ishant Sharma, Ashoke Dinda.