After opting to bat first, Kings XI Punjab got off to a steady start with Murali Vijay and Manan Vohra combining for a 45-run opening stand before Vijay perished to Sunil Narine for 28.
Manan Vohra looked in good nick and with a couple of reprieves, the opener scored 39 off 34 balls, but became Narine's second victim of the evening.
Glenn Maxwell then upped the ante for KXIP scoring 43 off just 22 balls and combined with Wriddhiman Saha for a 65-run stand for the third wicket.
However, Sunil Narine arrested the KXIP momentum by removing Maxwell and Saha (33) in the same over. Narine finished with impressive figures of 4-0-19-4.
David Miller's 11-ball 27 then helped KXIP post 183 for 5.
In chase of 184, KKR scored 31 runs for the opening wicket before Robin Uthappa departed for 17 to Anureet Singh in the fourth over.
Glenn Maxwell made telling impact with the ball as well removing Manish Pandey for 22. KKR went on to lose Gambhir in the next over bowled by Gurkeerat Singh Mann.
Yusuf Pathan and Andre Russell revived the KKR chase with a 53-run stand for the fifth wicket. Pathan scored 29 off 19 balls before falling to Beuran Hendricks.
With a brutal 21-ball 51-run knock, Andre Russell put his team in command but got out at the wrong time in the 17th over bowled by Axar Patel.
KKR scraped through for a one-wicket win courtesy Piyush Chawla 11-ball 18-run knock as the team went to of the table with 15 points.