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KKR will now meet Sunrisers Hyderabad (SRH) on Friday to decide who faces Chennai Super Kings in the final on Sunday.
With 74 needed from 48 balls, chinaman Kuldeep got rid of Rahane in the 15th over with Chawla then sending Samson back after he brought up his half century in 37 balls.
With the required run rate climbing up and set batsmen out, Royals, who have a thin middle order, could never recover.
Rahul Tripathi (20; 13b; 1x4, 2x6) helped Royals to a brisk start by tonking Russell (0/22) for a six in the first over and thereafter smacking the usually economical Sunil Narine (0/39) for two back-to-back sixes in the fifth over.
Rahane looked in effervescent touch at the other end, pulling and cutting M. Prasidh Krishna flawlessly in the fourth over after surviving a review when he was given out lbw by the umpire off Chawla on 14, two overs earlier.
Royals were 47/0 inside five overs before Tripathi - who also survived a review -- inexplicably chipped a googly back to Chawla for a soft dismissal.
In came Samson with the well-set Rahane batting and the duo looked on course to chase down 170 before they got out in quick succession and it was all downhill from there on.
Earlier, KKR rode on Karthik's well-paced fifty coupled with Russell's unbeaten 25-ball 49 blitz to recover from an early collapse. Russell came in to bat when KKR were trying to stem the rot through Karthik and Shubman Gill (28; 17b; 3x4 1x6) before the latter fell with the team on 106/5 in 14.2 overs.
The big-hitting West Indian smoked five sixes and three fours in the last five overs to take 55 runs and help the purple brigade post a challenging score.
Krishnappa Gowtham (2/15), Jofra Archer (2/33) and Ben Laughlin (2/35) got two wickets each for the Rahane-led side with leg-spinner Ish Sodhi conceding just 15 runs off his four overs.
Royals' bowlers made early inroads to reduce KKR to 51/4 after eight overs when Karthik and Gill got together.
The pair joined hands for a 55-run stand for the fifth wicket before Gill departed and Russell stepped on the gas.
Kolkata Knight Riders
S Narine st Klaasen b Gowtham 4
C Lynn c & b Gopal 18
R Uthappa c & b Gowtham 3
N Rana c Unadkat b Archer 3
K Karthik c Rahane b Laughlin 52
S Gill c Klaasen b Archer 28
A Russell not out 49
J Searles c Archer b Laughlin 2
P Chawla not out 0
Extras: (b4, nb1, w5) 10
Total: (7 wkts, 20 Overs) 169
Fall: 1-4, 2-17, 3-24, 4-51, 5-106, 6-135, 7-164
Bowling: K Gowtham 3-0-15-2; J Archer 4-0-33-2; J Unadkat 2-0-33-0; I Sodhi 4-0-15-0; S Gopal 4-0-34-1; B Laughlin 3-0-35-2
A Rahane c&b Kuldeep Yadav 46
R Tripathi c&b Piyush Chawla 20
S Samson c Javon Searles b Piyush Chawla 50
H Klaasen not out 18
S Binny c Chris Lynn b Prasidh Krishna 0
K Gowtham not out 9
Extras: (1w) 1
Total: (4 wkts, 20 overs) 144
Fall: 1-47, 2-109, 3-126, 4-130.
Did not bat: Archer, Gopal, Sodhi, Unadkat, Laughlin.
Bowling: Russell 3-0-22-0; Prasidh Krishna 4-0-28-1; Piyush Chawla 4-0-24-2; Sunil Narine 4-0-39-0 (1w); Kuldeep Yadav 4-0-18-1; Javon Searles 1-0-13-0.
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