Gautam Gambhir's men have won 10 of their last 11 in Kolkata and were always in control as they reached 171-7, with Yusuf Pathan top scoring on 42.
Piyush Chawla weighed in with 22 runs and the all-rounder was key with the ball as he took 4-32 to keep the visitors at bay.
Those figure are his best since the 4-17 in 2011 for Kings XI Punjab, as Kolkata limited Delhi to 158-6 and moved third in the Indian Premier League.
Kolkata were 38-1 by the time Gambhir edged Zaheer Khan (1-34) to Kedar Jadhav in the fifth over, with fellow opener Robin Uthappa reaching 32 before he was out lbw off Amit Mishra (1-20) four overs later.
Manish Pandey and Chawla each made 22 and the wickets continued to fall as Andre Russell (5) and Pathan went in the space of three overs.
But Delhi allowed Kolkata to add runs late in the innings, with Johan Botha's 17 coming off just five balls before being stumped at the death.
The away side then made a relatively laboured start. Manoj Tiwary (25) and Shreyas Iyer (40) scored 63 from their 9.5 overs before the former was caught by Yadav off Chawla.
At 64, Delhi's was the lowest score in this season's competition after 10 overs with the loss of just one wicket.
Veteran Brad Hogg (1-27) got off the mark to dismiss Iyer in the next over, with Jadhav (10) gambling on a six soon after only to find Botha at long-off.
Yuvraj Singh went for a duck three balls later and JP Duminy (25) became Chawla's fourth wicket - severely denting any hopes of a successful chase.
Angelo Mathews (22) was bowled by Russell (1-24), with Saurabh Tiwary (24) and Albie Morkel (5) unable to rescue Delhi.