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Narine had continued to trouble Watson (35) who was unable to read the spinner. He missed sweeping West Indian and was given LBW.
Watson and young Sanju Samson came together to build Rajasthan innings after losing two wickets early in their innings against Kolkata Knight Riders.
Both the Royals' batsmen had read the situation quickly and took calculated risks to make sure to keep the scoreboard ticking.
Electing to bat, Rajasthan Royals lost James Faulkner (1) and Ajinkya Rahane (6) early against Kolkata Knight Riders in the IPL match at the Eden Gardens on Friday.
Iqbal Abdulla dismissed Faulkner (1) soon after Sachithra 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.
Their campaign in doldrums, Knight Riders would be desperate to register a victory over a consistent Royals.
Midway into the extravagant T20 League, when faltering teams like Delhi Daredevils have started to get their act together, the Knight Riders have refused to learn from the mistakes, with captain Gambhir being adamant in his approach.
The latest of their seven losses was against the resurgent Daredevils who registered their second successive win, third overall, by seven wickets on Wednesday at Raipur.
It was Knight Riders' fifth defeat from as many away games. They now have an uphill task of winning six more matches if they want to earn a ticket to the playoffs.
That they have three away games, including one in Mumbai, and two 'home' games (vs RCB and PWI) at an unfamiliar venue -- Ranchi -- will make the case all the more difficult, and it will be a real test of character for skipper Gambhir.
On the other hand, Rahul Dravid has led the side by example so far and backed his little-known judicious-spending team to perfection, reminding one of what Shane Warne did in their triumphant season one (2008).
Rajasthan's back-to-back victories have earned them 12 points from nine matches and they are comfortably placed at third position in the table.
Shane Watson's red-hot form with the bat -- 101, unbeaten 98 and 41 in last three appearances -- is just coming at the right time. The Aussie vice-captain's contribution with the ball is also providing the team an edge.
The fact that Dravid-led team had a three-day break after their victory against RCB will put them in the right frame of mind as compared to KKR, who travelled to Chennai and Raipur before coming here.
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).