The visitors, chasing 178 to win, managed to score just 160 for six.
It was Rajasthan Royals' fourth successive win - after having started the tournament with three straight defeats.
It was Rajasthan Royals' 10th home win in 11 matches - the best record at home by any team in the IPL.
They also preserved their impeccable record of having not lost a match when defending a total of 150 or more.
It was also their fourth win over Chennai, the team they beat to take the title in the inaugural edition, in six matches.
For Shane Warne [ Images ], it was 22nd win as a captain in 35 matches - as opposed to just 12 defeats.
Warne's tactical acumen came to the fore yet again in his bowling changes, field placements et al.
As regards Chennai, it was their fifth defeat in seven matches, their third in succession, and jeopardises their chances of a semi-final berth.
The result though didn't affect the points table, with both Rajasthan and Chennai remaining on third and seventh respectively.
Chasing a formidable target, Chennai got off to a flier before losing their way midway through their innings.
Matthew Hayden [ Images ] (19), the man with the Mongoose, got the Chennai chase off to a flier smashing Sumit Narwal over long-on for a maximum.
The veteran batsman, however, didn't last long, Yusuf Pathan [ Images ] catching him off his own bowling in the fourth over.
However, the fifth over turned out to be hugely productive for the team from Chennai with Murali Vijay [ Images ] (42) taking a whopping 24 runs off Narwal, including three hits to the fence and two over it.
Vijay was, however, fortunate when Warne couldn't hold on to a catch at mid-on.
And as the field restrictions eased, Chennai saw themselves comfortably placed at 58 for one, the same score as Rajasthan at that stage.
Vijay and Raina put on 51 runs - off just five overs - for the second wicket before the former found himself short of the crease to a direct hit by Yusuf.
The Tamil Nadu opener's 28-ball knock was inclusive of four hits to the fence and two over it.
But despite him getting out, Chennai was comfortably placed at 76 for two after nine overs - heading into the first strategic timeout.
The comfort, however, didn't last long.
Shane Warne foxed Raina with a slower one and rattled his off stump in the first over after resumption to bring Rajasthan back into the match - it was his 37th wicket in the IPL, just second behind RP Singh's [ Images ] 41 dismissals.
The fall of two wickets in succession helped Rajasthan peg back the Chennai scoring rate to a great extent.
Dhoni and Subramaniam Badrinath [ Images ] (25) put together 44 runs 9off 36 balls) for the fourth wicket before the latter ran into his captain during the course of a run, a collision that resulted in the former being run out.
The timing of the dismissal was so bad that Dhoni was furious at Badri even as he left the crease.
However, Albie Morkel [ Images ] (28) eased the pressure to a considerable extent and brought his side back into the game with three successive sixes off Warne's last over.
The three maximums ensured the Australian spinner the dubious distinction of having conceded the most sixes in the IPL - 19, two more than Piyush Chawla [ Images ] (17).
Chennai needed just 27 runs off their last two overs with six wickets left.
But Badrinath mistimed a pull off Tait, hitting straight to Yusuf at midwicket to give Rajasthan a ray of hope.
And four balls later, Tait struck again, having the dangerous Morkel caught by Faiz Fazal at deep midwicket.
As a result of the two dismissals in the penultimate over, Chennai required a whopping 22 off the final over and it was a lost cause.
Earlier, a masterclass 80 by Naman Ojha [ Images ] helped Rajasthan Royals notch up a formidale total.
The home team made 177 for seven in their stipulated 20 overs.
Rajasthan lost the plot somewhat in the second half of their innings but managed to reach the target that their captain Shane Warne had envisaged at the toss.
Michael Lumb (30), who had given his side good starts in their last two games, began his aggression from the third ball of the innings, despatching Albie Morkel for a maximum over long-on.
The Hampshire batsman continued to hound his compatriot with a boundary left of mid-on and another maximum over the square-leg boundary.
However, Morkel, playing in his 100th T20 game, got his revenge in the final ball of his second over when he foxed Lumb with a slower ball and had him caught by Thilan Thushara at mid-off.
Naman Ojha smashed Muttiah Muralitharan [ Images ] over wide midwicket for the third maximum of the innings to ease the pressure.
As the field restrictions eased (after six overs), the home team had got off to a good start - at 58 for one.
Ojha ensured they maintained the momentum by going after Joginder Sharma - the bowler went for 23 in his firts two overs.
At the first strategic timeout Rajasthan had raced to 86 for one.
In the fourth ball after resumption Ojha smashed Suresh Raina over mid-on for his second maximum, the fourth of the innings.
Soon Ojha reached his third IPL fifty with a single off Shadab Jakati [ Images ] - the run also brought up the 100 runs of the innings, the fastest for Rajasthan in this campaign.
However, Jakati did manage a breakthrough in that over, haing Faiz Fazal (17) caught by Murali Vijay at long-on.
The second-wicket partnership yielded Rajasthan 53 runs in just seven overs.
The spinner came back to account for Yusuf Pathan (8) in his next over.
Yusuf was almost caught by Muralitharan off the first ball, when a mistimed pull shot from his blade saw the ball just fell short of the fielder at long-on.
However, the next time he mishit there was no reprieve as Raina made no mistake at short cover.
There was a period of lull after the two successive dismissals but Ojha soon broke free with two maximum off Jakati's final over.
Despite conceding 15 runs in his last over, Jakati did a pretty good job with figures of two for 30.
Ojha's brilliant knock came to an end in the 18th over, when he mistimed a Thushara delivery straight to Joginder Sharma at short fine-leg.
Ojha's 49-ball knock include six hits to the fence and five huge ones over it.
Adam Voges made a 19-ball 20 before Morkel accounted for him in the penultimate over.
And in a bid to accelerate, Rajasthan lost as many as three wickets in the final over of the innings bowled by Thushara.
Earlier, Rajasthan Royals' captain Shane Warne won the toss and elected to bat.
"It looks a good wicket and we look to put up a total of 165-170 plus and make it hard work for them," said Warne, adding, "The boys, to their credit, have worked really hard and we are confident of ourselves."
Warne's Chennai counterpart, MS Dhoni, seemed to concur.
"I would have liked to bat as well but am not disappointed at losing the toss," admitted Dhoni, adding, "We know the areas where we need to work on and it is more about motivating the boys and getting the confidence back."
Chennai Super Kings: MS Dhoni (captain), Matthew Hayden, Murali Vijay, Arun Karthik, Suresh Raina, S Badrinath, Albie Morkel, Shadab Jakati, Muttiah Muralitharan, Joginder Sharama, Thilan Thushara.
Rajasthan Royals: Shane Warne (captain), Naman Ojha, Michael Lumb, Yusuf Pathan, Faiz Fazal, Abhishek Jhunjhunwala, Paras Dogra, Adam Voges, Shaun Tait, Siddharth Trivedi, Sumit Narwal.