Kulasekara first got Robin Uthappa (8) caught by R Ashwin and then dismissed Jesse riders (9) to reduce Pune Warriors to 26/2 in four overs.
After being invited to bat, F du Plessis and Subramaniam Badrinath shared a solid 116-run stand for the first wicket, frustrating Pune bowlers.
Both batsmen slammed half century each as the visitors were seen reeling at the Chepauk stadium.
Marlon Samuels struck for Pune in the 16 th over as he got rid of both openers to revive visitors hope. Samuels sent back both batsmen in the same over reducing Chennai to 116/2 in 16 overs.
While Plessis made 58, Badrinath scored 57.
Capitalising on the breakthrough provided by Samuels, Ashish Nehra soon gave CSK third blow by dismissing Suresh Raina for a duck, with scorecard reading 119.
Skipper MS Dhoni then produced a fiery show to power his side to a challenging total.
CSK: Faf du Plessis, Wriddhiman Saha, Suresh Raina, MS Dhoni, Subramaniam Badrinath, Dwayne Bravo, Ravindra Jadeja, Doug Bollinger, Ravichandran Ashwin, Shadab Jakati, Nuwan Kulasekara
PWI: Robin Uthappa, Jesse Ryder, Sourav Ganguly, Marlon Samuels, Steven Smith, Angelo Mathews, Mithun Manhas, Bhuvneshwar Kumar, Rahul Sharma, Ashish Nehra, Murali Kartik