Brendon McCullum (66 off 44 balls) and Mahendra Singh Dhoni (41* off 27) propelled Super Kings to 192 for three before the spinners put up a stellar show to limit Kings XI to 95 for nine in 20 overs.
Kings XI showed little fight in the run chase as Ashwin (2/14) and Jadeja (3/22) ran through their batting on a helping pitch.
With the comprehensive win, Super Kings move to the top of the table with five victories from six games while Kings XI were handed their fourth loss in six matches.
The away team could never recover after suffering a major setback at the start of the chase, losing Virender Sehwag (1) and the in-form Shaun Marsh (10) to make it 35 for two.
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Ashwin and Jadeja came to the party there after, foxing the opposition batsmen one by one to guide their team to an easy win.
Opener Murali Vijay (34) hit some lusty blows as wickets kept tumbling at the other end and once he departed, it was all but over for Kings XI.
McCullum and Dwayne Smith (26 off 13) laid the foundation for a big score before captain Dhoni came up with a timely cameo to end the innings on a high.
While Super Kings batted well, Kings XI did not help their cause by offering loosing balls regularly besides being sloppy on the field.
The dangerous duo of Smith and McCullum gave another cracking start to their team and toyed with the promising bowling attack of Kings XI.
The visitors' move to open with leg-spinner Karanveer Singh did not pay off as he gave away 26 runs in his first two over before being taken off.
McCullum took medium pacer Sandeep Sharma to the cleaners in the next over, pulling him for a massive six over mid-wicket and cutting him for a boundary.
First change Anureet Singh picked up a timely wicket off Smith in fifth over and that put a halt to the onslaught from both ends.