McCullum ??? dropped by Mitchell Johnson early in his innings ??? smacked 66 off 44 balls as Chennai posted 192-3 in their twenty overs.
And Jadeja (3-22) and fellow-spinner Ravi Ashwin (2-14) ripped through the Kings XI line-up to secure an easy victory, restricting them to 95-9.
McCullum and Dwayne Smith gave Chennai a good start, adding 50 for the first wicket in just 4.4 overs. West Indies star Smith had scored 26 off 13 balls but bottom-edged a pull of Anureet Singh into his stumps.
Just before that, Johnson had spilled a skier from McCullum. He fumbled the initial attempt, flicked it up in the air with his boot, but then dropped it again.
Suresh Raina (29) helped the Kiwi add another 66 before McCullum holed out off Axar Patel.
Raina was run out, but MS Dhoni (41 not out off 27) and Jadeja (18no) scored a late flurry of runs to give Chennai an intimidating total.
The reply never got off the ground, Murali Vijay top-scoring with 31. Virender Sehwag gave his wicket away, checking his drive off Ishwar Pandey straight to Faf du Plessis at mid-off.
Ashish Nehra pinned Shaun Marsh in front for ten, and skipper George Bailey (1) nicked Jadeja behind.
David Miller (3) tickled the spinner to leg-slip, and Vijay, Kings XI???s last real hope, smacked Ashwin straight to Dwayne Bravo at deep mid-wicket.
The rest fell away, strangled by the spinners and unable to make any hay against the quicks, and Kings XI are now bottom of the pile.