Invited to bat, the Super Kings rode on Ravindra Jadeja's 28-ball unbeaten 44 and Mahendra Singh Dhoni's 16-ball 35 to post a challenging 155 for six.
Ravichandran Ashwin then shone with the ball, returning impressive figures of 3/20 to restrict the Scorchers to 142 for seven in 20 overs.
That the CSK got enough to defend was mainly due to the brisk 64-run sixth-wicket partnership, which came off just 30 balls, between Jadeja and Dhoni. This after the Scorchers spinners, led by Brad Hogg, had stifled the two-time IPL winners at the Chinnaswamy Stadium.
While the CSK skipper got out while going for another maximum in the final over, which also ended his crucial association with Jadeja, the left-handed all-rounder hit a six and a four to finish things off in style for the Super Kings.
Also Read
Dhoni hit four sixes while Jadeja found the fence four times and cleared it twice.
When their turn to bat came, the Scorchers lost Craig Simmons and Ashton Agar with 26 runs on the board. While Simmons was foxed by Ashish Nehra's slower ball, Agar had no answer to a quicker one from Ashwin.
At the start of 17th over, the Scorchers needed 58 off 24, but Nathan Coulter-Nile and Ashton Turner reduced the margin to 44 in the last three.
Just after completing a 33-ball sixth-wicket 50-run partnership with Coulter-Nile, Turner was run out due to Dhoni's smart work, putting to rest whatever little hopes Scorchers had of pulling off a shock win.
The Australian outfit is more or less out of contention.