Chasing a mammoth target (247) to win, the visitors eventually wound up at 223 for five in their stipulated 20 overs.
It was the home team's fourth win - their second straight - in nine matches in this edition and was a perfect reply to their 17-run defeat at Motera in the opening encounter between the teams this season.
It was also the Chennai team's third win in seven matches against the team from Rajasthan and moved them up to fourth in the table.
More importantly, it was Chennai's first ever win over Rajasthan on Indian soil, the latter having triumphed in all the four previous encounters.
As regards Rajasthan, it was their fifth defeat in nine matches, their second straight - Shane Warne's [ Images ] team had started the tournament with three straight defeats before rebounding with four straight wins - and they dropped to sixth in the table.
Naman Ojha [ Images ] provided stiff resistance with a defiant 55-ball 94 not out, a knock that was inclusive of eight hits to the fence and six over it.
But, in the end, even that wasn't enough.
Doug Bollinger, playing in his first match, was the pick of the Chennai bowlers with impressive figures of two for 15. In fact he was the lone bowler to survive a batting onslaught in the match.
Michael Lumb (37) ensured the Rajasthan chase began with the right intent, scoring as many as three boundaries in Morkel's first over.
However, Bollinger gave away just a single in his first over to put the pressure back on.
There was a lull before the Rajasthan batsmen broke the shackles in the fifth over by Sudeep Tyagi [ Images ], both Naman Ojha and Lumb helping themselves to a six each as they garned 18 runs.
The sixth over by Morkel fetched the visitors another 15 runs, with Ojha helping himself to three boundaries.
As the field restrictions eased, Rajasthan had made 62 without loss - Chennai had made 66 for one at that stage.
Chennai got the breakthrough in the next over, Morkel having Lumb caught by Aniruddha Srikanth at sweeper-cover.
In came Yusuf Pathan [ Images ] (4) and he faced just two balls - announcing his arrival with a boundary before a superb catch by Bollinger brought a premature end to his innings.
However, Ojha and Shane Watson [ Images ] (60) put together an aggressive 97-run partnership (off just 43 balls) for the third wicket to bring the visitors back into the game.
Ojha completed his fourth IPL fifty with a single off Shadab Jakati [ Images ] in the 11th over.
And Watson, the player-of-the-tournament in the inaugural edition but his playing in his first match in this edition, played an aggressive knock to keep Rajasthan's hopes alive..
The Australian's 25-ball knock was inclusive of five hits each to the fence and over it.
He was particularly severe in Muttiah Muralitharan's [ Images ] third over - the 15th over Rajasthan's innings - smashing three sixes and a boundary.
The second of those maximums helped him complete his fifth IPL fifty.
However, Bollinger came back to end Watson's resistance, cleaning up his compatriot's stumps with an off-cutter.
Muralitharan came back to have Faiz Fazal 94) caught by Srikkanth at cover-point.
And Bollinger had Abhishek Jhunjhunwala (7) caught by in his final over - the penultimate one of the innings - to all but seal the result in Chennai's favour.
Rajasthan required 35 runs off the last over - a lost cause in every possible way.
Earlier, Murali Vijay [ Images ] and Albie Morkel [ Images ] put the Rajasthan Royals bowlers to sword with their aggressive batting and helped Chennai Super Kings post a huge total. The home team had made a mammoth 246 for five in their stipulated 20 overs.
It was the highest ever total in the IPL - surpassing the 240 for five they had themselves made against Kings XI Punjab [ Images ] in the inaugural edition.
The first 10 overs of the innings cost Rajasthan 91 runs. The last 10 cost them a whopping 155 runs - with 76 coming off the last five.
The home team's innings contained 17 sixes - the most in an innings in the IPL.
And that underlines Chennai's dominance.
Vijay scored what was the fourth fastest hundred in IPL history - off just 46 balls.
The Chennai opener's eventual effort - 127 - came off just 56 deliveries, was inclusive of eight boundaries and 11 maximums and was a perfect follow-upto his 78 in the previous game against Royal Challengers [ Images ] Bangalore, an effort that had had won him the man-of-the-match award.
It was the highest ever score by an Indian in the tournament.
It was also only the third occasion that an Indian had made a hundred in the IIPL - after Manish Pandey's [ Images ] unbeaten 114 against Hyderabad in the second edition and Yusuf Pathan's 100 against Mumbai Indians [ Images ] earlier in the tournament.
Morkel played a perfect foil, scoring an aggressive 62 (off just 34 balls), a knock that was inclusive of three hits to the fence and five over it.
The duo put together a stand of 152 runs for the third wicket - a partnership that came off just 66 balls and was the second highest in IPL history.
Vijay began on an aggressive note, hitting a boundary past backward point off Yusuf Pathan's third ball.
The right-hander stepped up the gear in the second over (by Sumit Narwal), lofting the bowler over mmidwicket fence for a maximum and following that up with successive boundaries, the first over midwicket and second past the covers fielder.
Vijay got yet another maximum in Pathan's second over, this time straight over the bowler's head and into the sightscreen.
His second boundary, a mishit of Shane Watson that went over the short third man, helped the Australian legend surpass the 1000-run mark in the IPL.
And he celebrated reaching the landmark by smashing Watson over the midwicket for a maximum.
Shrikant Wagh's opening over witnessed Hayden going full throttle, hitting three successive boundaries, before the bowler had the last laugh, having him caught by Watson at extra cover.
The opening wicket stand yielded Chennai 62 runs (off just 35 balls) and as the field restrictions eased the home team was sitting pretty at 66 for one, good enough reason for Shane Warne to take a strategic timeout.
Suresh Raina (13) didn't last long.
But he managed to become the highest scorer in IPL history during his innings before Warne had him caught by Tait at point.
The scoring rate dipped for a few overs after Raina's dismissal before Albie Morkel eased the pressure with a massive six off Abhishek Jhunjhunwala (in the 12th over).
The South African did an encore in the next over by Warne, on this occasion going over deep square leg.
Vijay, who had gone quiet after his early blast, returned to aggressive ways with a maximum two balls later, the shot helping him register his second successive fifty.
The Tamil Nadu batsman celebrated the occasion by hitting Pathan for a boundary and a six off successive balls. Morkel also helped him to a similar pattern in the same over - the over cost Pathan (and Rajasthan) 22 runs.
Tait's next over - the 15th of the innings - cost Rajasthan another 19 runs, and that included two massive sixes for Vijay.
As the second timeout was taken (after 15 overs) Chennai had already ensured themselves a huge total - 170 for two.
The first over after resumption - by Narwal - cost Rajasthan another 26 and that included four sixes, three for Vijay.
And though three wickets fell in the final over, the duo had ensured Chennai ended their innings on an emphatice note.
Earlier, Chennai Super Kings' captain Mahendra Singh Dhoni [ Images ] won the toss and elected to bat first.
It was the seventh time in nine matches thus far that Shane Warne had called incorrectly.
"It's a belter of a track but there's also some bounce for the seamers. I see plenty of runs coming," reasoned Dhoni.
His Rajasthan counterpart seemed to concur.
"Looks a good wicket and we are looking to bounce back," he said.
Chennai Super Kings: MS Dhoni (captain), Matthew Hayden, Murali Vijay, Suresh Raina, S Badrinath, A Srikkanth, Albie Morkel, Muttiah Muralitharan, Shadab Jakati, Doug Bollinger, Sudeep Tyagi.
Rajasthan Royals: Shane Warne (captain), Naman Ojha, Michael Lumb, Shane Watson, Faiz Fazal, Abhishek Jhunjhunwala, Abhishek Raut, Shrikant Wagh, Yusuf Pathan, Shaun Tait, Siddharth Trivedi [ Images ].