Cummins bowled a superb 19th over followed by Bhuvneshwar successfully defending 12 in the final over.
The spinners combined for eight boundary-less overs that fetched them four wickets for just 33 runs.
Marcus Stoinis once again rescued a win as Lucknow Super Giants emerged triumphant with a four-wicket win against Mumbai.
India announce squad for T20 World Cup; Pant and Samson included, KL Rahul misses out.
The target of 154 runs was a cakewalk for KKR as the Kolkata batters chased down the total in just 16.3 overs.
Chennai Super Kings move to third on the points table but are tied with four other sides on ten points.