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 at the Dubai International Cricket Stadium.
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.
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.
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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.