Sent into bat, Ben Hilfenhaus (2/8) produced a stunning opening spell to dent Rajasthan's prospects at the start.
Hilfenhaus scalped two vital wickets of Rajasthan skipper Rahul Dravid and Shane Watson early during his breathtaking opening spell of four overs which yielded just eight runs.
Dravid was Hilfenhaus' first victim as he fell in the second over, top-edging one to Michael Hussey at mid-off.
Hilfenhaus then accounted for dangerman Shane Watson cheaply three overs later to derail Rajasthan's innings which was marred by three brief rain interruptions at the Sawai Mansingh Stadium.
Watson was brilliantly caught by a diving Ravichandran Ashwin at the third-man boundary as the batsman went for a huge heave over square-leg only to get a leading edge.
In-form Ajinkya Rahane (17) too perished soon in search of quick runs, again caught by Ashwin off Yo Mahesh (2/21) as Rajasthan slipped to 43 for three in the ninth over.
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Stuart Binny, however, tried to force a comeback with a fierce counter-attack and thrashed Dwayne Bravo for two boundaries and a six to pick up 18 runs off his opening over.
But Binny departed in the next over in search one too many, caught by Suresh Raina off Mahesh.
Brad Hodge and Johan Botha then added 32 runs for the fifth wicket to give impetus to Rajasthan's innings before the two fell in quick succession.
While Botha was cleaned up by Ravindra Jadeja, Hodge's 28-ball 33-run knock was cut short by Ashwin.
Hodge top-scored for Rajasthan with 33 off 28 balls, while Binny played a vital 18-ball 27-run knock in the middle.