Defending 172-run target on a slow and turning Eden Gardens pitch, Narine (3/26) returned his best figures of the season and was ably supported by left-arm chinaman Yadav (2/28) as Sunrisers could only muster 149 for eight.
Both KKR and Sunrisers finished their campaign on 16 points from 14 games, which was enough for both the teams to qualify for the play-offs.
Even though Sunrisers skipper David Warner (18) was cleaned up by Narine in the fourth over, Dhawan looked in ominous touch before young Yadav triggered the collapse dismissing the left-handed batsman.
It was a master stroke from KKR captain Gautam Gambhir to bring the rookie chinaman spinner into the squad in place of Piyush Chawla as Yadav, who was playing his second match after a more than a month's gap, did not disappoint.
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(REOPENS DEL 65)
Left-arm spinner Shakib Al Hasan (134) then cut short Yuvraj's innings before Deepak Hooda was run out in the next over as Sunrsiers chase fell by thenway side.
Moises Henriques (11) became Narine's third victim when he went through the Australian's defence.
Earlier, Yusuf Pathan struck his third half-century of the ongoing IPL before some brilliant death bowling by Sunrisers Hyderabad restricted Kolkata Knight Riders to 171 for six.
The duo hammered the inexperienced Sunrisers spin attack and at 141 for three, KKR looked on course for a 200-plus total after being put in by David Warner.
But Sunrisers famed death bowling came to the fore as Bhuveneshwar Kumar (2/31) broke the partnership dismissing Pandey with Kane Williamson taking a splendid diving catch at point.
Young left-arm pacer Barinder Sran (1/31) also gave fine support at the death along with Mustafizur Rahman (1/32) that denied KKR extra 15-20 runs.