McCullum took the Sunrisers' bowling apart, blasting seven fours and nine sixes in an unbeaten 100 off 56 balls. The innings included some vintage McCullum ramp shots - two of them coming off the bowling of Boult - and plenty of power hitting.
It was the second time McCullum has scored a century in the IPL.
Chennai posted 209 off their 20 overs, a total that was never in reach of the Sunrisers who finished at 164-6, with Williamson contributing an unbeaten 26 off 18 balls in a losing effort.
Boult picked up the wicket of Chennai's captain MS Dhoni to finish with figures of 1-34 off four overs.