Mohit Sharma was the wrecker-in-chief for CSK as he claimed three wickets in his four-over spell giving away 31 runs.
Ravindra Jadeja took two wicket in his four-over spell.
Chasing 149-run target, opener Dwayne Smith gave a solid start to Chennai Super Kings as he scored 44 off 35 balls.
MS Dhoni struck a quickfire 26 to guide Chennai Super Kings to a five-wicket victory.
Skipper Shane Watson smashed 51 off 36 balls to take Rajasthan Royals to 148/8 against Chennai Super Kings.
Rajasthan Royals skipper Shane Watson won the toss and opted to bat against MS Dhoni-led Chennai Super Kings.
Rajasthan Royals cheerleaders during the Chennai Super Kings and the Rajasthan Royals match.