The Sunrisers hit 160-7 before the Knight Riders, who have already qualified for the playoffs, reached 161-6 with around five overs remaining.
Hyderabad got off to a bad start at the crease when David Warner was dismissed for four runs, but Shikhar Dhawan (29), Naman Ojha (26), Venugopal Rao (27) and Darren Sammy (29) helped to boost their score.
However, Jason Holder (16) was the only batsmen to get into double figures in the lower order as the Sunrisers finished with a modest total.
A mammoth knock of 72 off just 22 balls from Yusuf Pathan made up the bulk of the Knight Riders' runs when it was their turn to bat, with Robin Uthappa (41) and Gautam Gambhir (28) also helping their team towards victory.
Suryakumar Yadav (12) then came in to make sure that Kolkata extended their winning run ahead of the playoffs.
Karan Sharma took an impressive four wickets for the Sunrisers, while Holder also got in on the act.