The 2013 IPL finalists were in complete control of the match but for last three overs of the Heat innings and that prevented the match from becoming a lop-sided affair.
Chasing a modest 138 to win, Chennai sauntered to finish line with 25 balls to spare as they scored their third successive win to consolidate their top position in Group B.
Opener Michael Hussey top scored for them with an unbeaten 55-run knock and shared a solid 75-run stand for the opening wicket with Murali Vijay (42).
Vijay, who played more aggressively in the opening stand, faced 27 balls and hit five fours and two sixes while Hussey took 48-balls for his measured innings which had seven boundaries.
Suresh Raina came up with a 23-run cameo before being trapped by Daniel Christian while skipper Mahendra Singh Dhoni (13) finished the match in style with a six off Ben Cutting.
After electing to bowl, Chennai had the Australian team on the mat as they had reduced Heat to 66 for six but some scintillating batting by Ben Cutting made it a contest as he led the side to respectable 137 for seven.
Cutting hit five sixes in his blistering 25-ball 42-run knock and added 71 runs with Chris Hartley (31) for theseventh wicket.
The spin trio of R Ashwin (1/10), Ravindra Jadeja (2/18) and Suresh Raina (19) did a brilliant job for CSK as they gave away just 37 runs in their combined 11 overs and shared four wickets among them.
Cutting and Hartley's batting overshadowed the splendid work done by CSK spinners as they snatched the momentum from CSK after being reduced to 87 for six in 17 overs.
It all started in the Dwayne Bravo when Cutting smashed him for two sixes to bring up the hundred. A similar treatment was meted out to paceman Mohit Sharma in the last over.
Hartley also played his part as he hit consecutive fours off Sharma before holing it out in the last ball.
Brisbane Heat have suffered their third defeat in a row and are languishing at the bottom of the table.

Chennai Super Kings: Mahendra Singh Dhoni (capt), Mike Hussey, Murali Vijay, Suresh Raina, Subramaniam Badrinath, Dwayne Bravo, Ravindra Jadeja, Albie Morkel, Jason Holder, Ravichandran Ashwin, Mohit Sharma.
Brisbane Heat: James Hopes (capt), Joe Burns, Daniel Christian, Chris Lynn, Chris Hartley, Ben Cutting, Cameron Gannon, Chris Sabburg, Dom Michael, Nathan Hauritz, Matthew Gale.


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