After restricting Rajasthan to 126 for six, CSK rode on Albie Morkel and Srikkanth Anirudha's late bursts to romp home with 11 balls to spare.
However, CSK's run chase were off to a bad start as they lost wickets at regular intervals to totter at 84 for six at one stage.
Chasing a modest total, CSK were dealt an early blow when Shane Watson went through the defence of a struggling Murali Vijay in the first over.
New man in Suresh Raina (23 off 17) played a cameo before he was brilliantly caught by Ajinkya Rahane off Pankaj Singh.
Image: Chennai Super Kings batsman Srikant Anirudha celebrates the victory over Rajasthan Royals during a IPL match between Rajasthan Royal s and Chennai Super King at Swai Mansingh stadium in Jaipur on May 10, 2012.
Scorecard | IPL 2012