Rajasthan had defeated KKR by 22 runs in their earlier meeting a few days back.
Chasing a target of 132, Kolkata Knight Riders reached the target with four balls to spare thereby notching up their second victory in the cash-rich league.
With 15 needed off the last two overs, Shakbi Al Hasan (16) hit a hige six over deep mid-wicket off Amit Singh get KKR close to the target.
Shakib got out off the very next delivery but a delicate late cut from Yusuf Pathan levelled the scores with only a single needed off last over. It was left to Ryan ten Doeschate, who hit a huge six off Ankit Chavan over deep square leg to clinch the issue.
Jacques Kallis (31, 39 balls, 3x4), Manvinder Bisla (29, 29 balls, 3x4) and Manoj Tiwary (24, 18 balls 1x4, 1x6) made useful contributions to help KKR win on a track which wasn't conducive for batting.
KKR skipper Gautam Gambhir started off the chase on a positive note hitting offie Johan Botha for two boundaries.
First was an inside-out hit over extra cover while the next was square cut. However, Gambhir responded a touch late to a call for single by Kallis as Rahul Dravid's direct show found his opposite number well short.
With pitch offering a fair bit of turn but KKR batsmen didn't stop playing shots knowing fully well that getting bogged down was like inviting trouble.
Bisla played and missed a few but in between hit a few boundaries. Kallis hit the best shot of the day—straight drive off medium-pacer Amit Singh.
Kallis who scored 31 was playing the role of a sheet anchor to perfection when he was declared leg before off Botha when he tried to sweep against the turn.