After opting to bowl, Bravo (2/19), Jadeja (2/23), Deepak Chahar (2/28) and Harbhajan Singh (2/31) shared eight wickets between them to keep DC in check.
To make matters worse for DC, their star batsmen Rishab Pant (38 off 25) and Keemo Paul failed to create an impact. However, towards the end, Amit Mishra (6 not out) and Ishant Sharma (10 not out off 3 balls) struck great shots to take the Delhi to a respectable 150-run mark.
Sent into bat, DC made a shaky start with Prithvi Shaw (5) and Shikhar Dhawan (18 off 14) adding 21 runs in 2.3 overs before the former was caught plumb in front of the wicket by Chahar.
Shaw's dismissal opened the floodgates as DC lost three wickets in quick time to slump to 75 for four in 11.3 overs.
Dhawan was the next to depart, caught by Mahendra Singh Dhoni off Harbhajan and then Colin Munro (27) was holed at deep square-leg by Bravo off Jadeja as the South African went for a slog sweep.
Skipper Shreyas Iyer (13 of 18) tried to anchor the innings but he too fell while going for a big shot, caught by Suresh Raina off Imran Tahir (1/28) in the 12th over.
The new man in, Axar Patel departed in the next over, hitting a short delivery of Bravo straight to Tahir at third man.
Pant and Sherfane Rutherford (10) shared 22 runs for the sixth wicket but CSK didn't allow the Delhi outfit to get any momentum, picking up wickets at regular intervals to rattle their innings.
Rutherford became Harbhajan's second victim, followed by Keemo Paul who was cleaned up by Bravo's perfect yorker in the 18th over.