Electing to bat at the M A Chidambaram stadium, McCullum reached his century in the last ball of the innings, the belligerent knock consuming just 56 deliveries.
Two-time champions CSK put up a formidable 209 for four and then restricted SunRisers Hyderabad to 164 for six in 20 overs for their second victory in as many games.
Skipper Mahendra Singh Dhoni smashed 53 off 29 balls while briskly adding 63 runs for the third wicket with the New Zealander. McCullum had stands of 75 with his opening partner Dwayne Smith (27) and 60 with Suresh Raina (14), respectively.
Off a full length delivery by Trent Boult, McCullum jabbed it to the covers for a single to bring up a well-deserved century.
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McCullum struck nine sixes and seven fours during his stay in the middle. Dhoni, who smashed Karn Sharma for three sixes in the 18th over, hit the maximum four times besides picking as many boundaries.
The hosts had a good start and exploded in the death. McCullum was his usual self, often running down the track to unsettle the bowlers.
While Super Kings didn't tinker with the XI that beat Delhi Daredevils narrowly on Thursday, SunRisers Hyderabad's Kane Williamson and Trent Boult made IPL debuts, Ravi Bopara got a game ahead of Eoin Morgan, and Steyn missed out.
When their time to bat came, SRH were off to a sedate start with openers David Warner and Shikhar Dhawan putting on 30 runs in four overs before the Indian was sent back by Mohit Sharma.