The Royals were sent into bat first and made 144-6 from their 20 overs, Brad Hodge top scoring with 46.
It looked an achievable target but the Knight Riders lost two the two early wickets of Mavinda Bisla for 1 and key man Jacques Kallis for a golden duck to Rahul Shukla.
England batsman Eoin Morgan led the resistance to give his side hope with 51 off 38 balls but the tail fell away cheaply and the Knight Riders were dismissed for just 125 as the Royals bowled them out with an over to spare.
Victory for the Royals mean they are the early IPL table toppers, with two wins from two.
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