In pursuit of 140-run, the visitors took the game home with 37 balls to spare. This victory turned out to be the biggest in this season so far, in terms of balls remaining.
The win, which took KKR to the top of the table with eight points from five matches (4 wins and 1 loss), was the best of this season in terms of the number of balls to spare.
Chasing 140 for a win, Narine (47) and Lynn (50) shared 91 runs for the opening stand in 8.3 overs to take the game away from Rajasthan. Narine contributed 47, his best of this IPL season, from 25 balls from which he hit six fours and three sixes while Lynn made an exact 50 from 32 deliveries, with the help of six boundaries and three sixes.
Earlier, Steve Smith scored an unbeaten 73 to anchor Rajasthan to 139 for 3. It was his first half-century of the season after the home side were invited to bat on a tricky track. He shared 72 runs in 10.4 overs with opener Jos Buttler (37 off 34 balls) for the second wicket after captain Ajinkya Rahane was out cheaply for 5 in the second over.
The home side were 56 for 1 at halfway stage but increased the scoring rate at the back end of the innings to add 83 runs from the next 10 overs with Smith scoring the bulk of the runs. However, they were immediately pushed at the backfoot as soon as the match started as Rahane was trapped LBW by Prasidh Krishna when the scoreboard read just 5.
Buttler hit a couple of fours in the fourth over bowled by Krishna and after that runs were hard to come by before one-down Smith hit another couple of boundaries in the ninth over off chinaman Kuldeep Yadav.
Smith reached to his 50 off 44 deliveries in the 15th over and after that, he opened up his arms in search of runs. Ben Stokes remained not out on 7 off 14 balls and shared 34 runs with Smith from 4.2 overs for the unconquered fourth wicket.