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The match is important for both sides as a victory will bolster their play-off chances while a defeat would bring them one step closer to the exit door.
The hosts overcame a 34-ball 91 from Hardik Pandya to record a win after six defeats
The Rohit Sharma-led side have been KKR's nemesis ever since the tournament began, racking up a mammoth 18 wins to KKR's five in 23 meetings.
None of the CSK top-order batsmen got going in the chase of 156, with Malinga and the Pandya brothers wrecking maximum damage.
The former left-arm bowler was, however, guarded when talking about his country Sri Lanka's chances in the showpiece event.
Rajasthan would be taking heart from the four-wicket win over Mumbai Indians at their own den last Saturday and will hope to get the better of their rivals once again, this time at home.
Dimuth Karunaratne's leadership in Sri Lanka's spectacular Test series win in South Africa tilted the scales in his favour.
The World cup squad will be announced Thursday.
Pant has been mum on being ignored for the World Cup in favour of Dinesh Karthik and it would be interesting to see how the 21-year-old responds to the disappointment.