With a blistering 85 off 39 balls, Sunil Narine took the lead, and young rookie Angkrish Raghuvanshi chipped in with 54.
Big-hitting performances from Andre Russell and Rinku Singh helped Kolkata end just five games short of Sunrisers Hyderabad’s IPL record total.
With 55, Rishabh Pant led Delhi in scoring as they suffered a crushing defeat.
Kolkata’s massive score was achieved barely one week after Hyderabad broke the previous IPL record of 263-5 established by Royal Challengers Bangalore in 2013 with a record 277-3.
The 2012 and 2014 IPL champions, Kolkata, have won all three of their games this season and are now atop the 10-team standings.