Rahul sustained a wrist injury during training in Melbourne on Saturday.
Delhi made three changes by bringing in a fit-again Rishabh Pant, Shimron Hetmyer and Daniel Sams. KXIP replaced Chris Jordan with Jimmy Neesham.
Having lost two tight games they should have won at the start of the season, KXIP managed to get on the right side of the results in the last couple of games, although it was too close for comfort by their own admission.
The win ended CSK's three-match losing run, while Kings XI slipped to the bottom place.
The camaraderie between Kumble and Rahul, with both coming from Bengaluru, should also help the team.
Kohli confirmed that the side would not tinker with their line-up for in the initial matches of the T20I series against the Black Caps starting on Friday at Eden Park, Auckland.
Dhawan was under some pressure before the third T20 International and a smashing half-century will keep him in the mix for the upcoming series where Rohit Sharma will be back from his break.
Dhawan, who will be leading Delhi in their Ranji Trophy game against Hyderabad, is back after recovering from a knee injury sustained during the Syed Mushtaq Ali Trophy, which required 25 stitches.
Rahul's ascendancy to captaincy was expected after Ravichandran Ashwin was traded to Delhi Capitals last month.
Rahul interacted with Pandya after India's 67-run win over West Indies in the series decider at the Wankhede.