Put into bat, Chennai scored 140 for six, thanks mainly to opener Smith's 28-ball 50 and Jadeja's crucial 36 not out lower down the order and then shot Rajasthan out for 133 in 19.5 overs at Dubai International Cricket Stadium to post their second consecutive win in the tournament.
Number 10 batsman, Dhawal Kulkarni, who top-scored for Rajasthan with an unbeaten 28 from 19 balls, threatened to take Rajasthan to an unlikely win by hitting a huge six in the final over to take his side to within nine runs from the last two balls. But, the number 11 batsman Pravin Tambe (2) was run out in the penultimate delivery to end the match.
Jadeja was the main tormentor of Rajasthan batsmen with his left-arm spin bowling with figures of four for 33 in his four overs, including two crucial wickets -- that of captain Shane Watson (7) and Sanju Samson (16) -- from consecutive balls in the seventh over.
Ishwar Pandey, Ravichandran Ashwin, Ben Hilfenhaus and Mohit Sharma chipped in with a wicket each as Chennai bowlers made life difficult for Rajasthan batsmen with a disciplined effort.
Chasing 141 for a win, Rajasthan began on a bright note but lost wickets early on to put themselves on the backfoot. They failed to stitch any substantial partnership with 28 for the ninth wicket being the highest.
None of the Rajasthan batsmen could put up any resistance with number 10 Kulkarni being the top scorer and half of their side were back at the pavillion at 63 for five in 10.5 overs.
Some of Rajasthan batsmen, including captain Watson, went for big shots which led to their downfall and inability to save wickets.
From a bright start, Rajasthan were slumped to 57 for four at the halfway mark, needing 85 from the last 10 overs with six wickets in hand.
Any hopes of a Rajasthan victory was as good as over after Steven Smith (19) was out in the 13th over. Rajat Bhatia gave some fight with a belligerent 20-ball 23 which was studded with a four and a six but that turned out to be delaying the inevitable.
Earlier, the highly rated Chennai top order batting suffered a collapse after opener Smith's scintillating display as they could score 140 for six.
Smith (50) tore into Rajasthan bowling attack with an impressive exhibition of strokeplay at the top but his batting colleagues failed to capitalise on the strong start after being put into bat.
Brendon McCullum (6), Suresh Raina (4), Faf du Plessis (7) and captain Mahendra Singh Dhoni (5) were out cheaply on a slow pitch as Chennai, the team which possessed one of the strongest batting line-ups this season, failed to put up a big score.
But for Jadeja , who scored an unbeaten 36 off 33 balls lower down the order, Chennai score would have been even lower.
Half of their side were back in the pavillion just after the halfway mark as they were reduced to 74 for five in 11.1 overs. Their biggest partnership was the 39 between Jadeja and Ravichandran Ashwin (9 not out) for the unconquered seventh wicket.
Smith scored exactly 50 from just 28 balls with the help of six fours and three sixes. He was out in the eighth over off Stuart Binny just after smashing the bowler for a six.
James Faulkner suffered the most from the blade of Smith who hit four successive boundaries off the bowler in the sixth over which yielded 19 runs.
Rajasthan, however, came back into the match with Rajat Bhatia taking the wicket of Raina.
Chennai then lost the wickets of du Plessis and Dhoni in the 11th and 12th overs to find themselves in a precarious position at 74 for five.
Mithun Manhas (10) fell in the 15th over and the responsibility of taking Chennai to a respectable score was left to Jadeja and Ashwin.
For Rajasthan Rajat Bhatia was the most successful bowler with two wickets for 13 runs. Faulkner, Pravin Tambe and Stuart Binny chipped in with a wicket each.