With this win, Chennai jumped to the top of the table with 16 points from 12 matches, while Rajasthan will continue to occupy the third spot with 14 points from 13 games.Chennai thus avenged their eight-wicket loss to Rajasthan in Ahmedabad last month.
Opting to bat, McCullum smashed a quickfire 81 before Chris Morris (3/19) produced a brilliant display with the ball for Rajasthan Royals to restrict Chennai to a modest 157 for five.
But Chennai rode on Jadeja's fine spin bowling performance and some brilliant ground fielding to restrict Rajasthan to 145 for nine.
Chasing the modest target, Rajasthan's innings just fell apart after a steady start.
Ajinkya Rahane (23) and Shane Watson (28) shared 37 runs for the opening wicket before the visitors lost the plot.
Rahane top-edged a Mohit Sharma (3/25) short delivery to a running Dwayne Bravo at deep square-leg in the sixth over before an over later skipper Steven Smith was bowled by Jadeja.
The turning point in the match came in the form of Watson's dismissal off Jadedja. Bravo pulled off a brilliant one-handed catch at long-off that was destined to go over the ropes to sent the home crowd into a frenzy at MA Chidambaram stadium.
Jadeja picked up his third wicket when he dismissed Karun Nair (10), who looped one straight to Ravichandran Ashwin at short fine-leg in the 12th over.
Jadeja was once again at the thick of things when Deepak Hooda hit a full toss straight to Suresh Raina at long-on in the first delivery off the 15th over.
Samson (26 off 17), James Faulkner (16 off 13) and Chris Morris (16 not out off 10) played good hands but it was not enough to take Rajasthan home as Bravo (2/43) scalped two wickets towards the end to ensure Chennai's win on their last home match.
Earlier opting to bat on familiar conditions, Chennai did not have the best of starts as they lost their first two wickets inside the fourth over with the scoreboard reading just 15.
Dwayne Smith (6) was the first to depart when he was holed out at mid-on by a diving James Faulkner off Ankit Sharma's (1/31) bowling in the third over.
In the next over, the Chennai outfit suffered another blow in the form of Raina, who managed to hit a length delivery off Morris to Faulkner at mid-off.
Thereafter, McCullum and Faf du Plesis (29 off steadied the ship with a 101-run stand for the third-wicket.
Initially McCullum and Du Plesis played cautiously and according to the merit of the ball.
McCullum opened up his arms in the sixth over smashing Pravin Tambe for two huge sixes in his opening over.
After a lull of four overs, McCulllum again opened up and struck two consecutive fours in Faulkner's second over.
McCullum continued in his aggressive vein and clobbered Rajat Bhatia for a four and six in the 14th over to take Chennai forward.
Du Plesis, on the other hand, played the second fiddle before he was run out by Watson in the 17th over.
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