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Royals batsmen failed to put on any substantial partnerships during their innings after losing two early wickets and set a modest 133-run target for the hosts KKR.
Sachithra Senanayake was the pick of Kolkata bowlers, taking two Royals wickets for 26 runs in his four overs. Rajat Bhatia (1-21), Sunil Narine (1-20), Iqbal Abdulla (1-22) and Jacques Kallis (1-25) also picked up a wicket apiece.
Young Sanju Samson top-scored for the visitors with 36-ball 40 as he hit two maximums and a four in his innings. Shane Watson (35) and Owais Shah (24) also contributed handsomely in their team's effort.
Sachithra Senanayake struck again to dismiss Dishant Yagnik (10) in the thirteenth over to reduce Rajasthan to 83/4 in 12.2 overs.
Sunil Narine dismissed Shane Watson (35) after the Aussie helped Rajasthan fortify their innings. Narine troubled Watson, who was unable to read the spinner, for long before finally trapping the Aussie leg before.
Watson, who hit four boundaries in his run-a-ball knock, and young Sanju Samson came together to build the Rajasthan innings after losing two early wickets.
Both the Royals' batsmen had read the situation quickly and took calculated risks to make sure to keep the scoreboard ticking.
Rajasthan lost James Faulkner (1) and Ajinkya Rahane (6) early.
Iqbal Abdulla dismissed Faulkner (1) soon after Senanayake struck in the previous over to reduce Rajasthan to 27/2 in 4.3 overs.
Senanayake gave the hosts an early breakthrough when he outfoxed Rahane in the fourth over.
Earlier, Rajasthan Royals skipper Rahul Dravid won the toss and decided to bat against Kolkata Knight Riders in the defending champions' last league fixture at the Eden.
Rajasthan have made three changes in their team from the last game citing the slow and low wicket at the Eden. Brad Hogg replaced Brad Hodge, Ankit Chavan came in for Ajit Chandila and Dishant Yagnik included in Sreesanth's place.
Hosts KKR have included Sachithra Senanayake and left out Brett Lee for this game, whereas, spinner Iqbal Abdulla replaced pacer L Balaji.
Kolkata Knight Riders: Gautam Gambhir (Capt.), Manvinder Bisla (wk), Yusuf Pathan, Jacques Kallis, Eoin Morgan, Debabrata Das, Rajat Bhatia, Sumit Narwal, Sunil Narine, Iqbal Abdulla, Sachithra Senanayake.
Rajasthan Royals: Rahul Dravid (Capt.), Ajinkya Rahane, Sanju Samson, Shane Watson, Stuart Binny, Owais Shah, James Faulkner, Siddharth Trivedi, Brad Hogg, Ankit Chavan, Dishant Yagnik (wk).