After inserting Delhi Daredevils at the Feroz Shah Kotla, Kolkata Knight Riders struck early. Sunil Narine's wicket of JP Duminy had reduced the home team to 22 for 2.
For the first time this season, Chawla turned in an impressive performance with figures of 2 for 27. He also recorded the distinction of taking 100 IPL wickets.
Umesh Yadav was adjudged Man of the Match for his figures of 2 for 18.
Not long after Tiwary's dismissal, Yuvraj Singh got out stumped in bizarre fashion off the bowling of legspinner Piyush Chawla. He made 21 off 19 balls.
Manoj Tiwary threw away a good start after making a 28-ball 32. Delhi Daredevils lost the plot after his wicket.
Angelo Mathews took 20 runs off the penultimate over bowled by Narine to take Delhi Daredevils to a competitive 146 for 8.
Medium pacer Domnic Joseph took wickets of Robin Uthappa and Manish Pandey in quick succession to give some hopes to Delhi Daredevils.
However, Kolkata Knight Riders captain Gautam Gambhir held his end up and scored his third fifty in four matches. The visitors won by six wickets with 11 balls to spare and registered their third win this season.