Raina scored 20 before falling to Plessis who earlier got Faf du Plessis stumped out after his fiery knock of 43 that included two sixes and five boundaries.
Earlier, Angelo Mathews struck for Pune to remove Murali Vijay after strong start by Chennai Super Kings.
Mathews got Vijay caught by Ashok Dinda at long on after a solid 43-run partnership between him and Plessis for the first wicket.
Chennai Super Kings have brought in Nuwan Kulasekara and Yo Mahesh in place of Doug Bollinger and Shadab Jakati.
Pune captain Sourav Ganguly said he would have batted first too. Murali Kartik has come back into the Pune squad in place of out-of-form Manish Pandey.
Team Pune will be aiming to nip their batting worries in the bud when they take on defending champions Chennai at the Subrata Roy Sahara stadium on Saturday. After a spectacular start to the season with two thumping wins, the hosts were brought down to earth by a seven-wicket defeat to Punjab at Mohali on Thursday.
On the other hand, Chennai Super Kings came back from the dead in the previous game against the Royal Challengers Bangalore to make it two wins in four games.
Pune Warriors: Jesse Ryder, Sourav Ganguly, Robin Uthappa, Angelo Mathews, Marlon Samuels, Mithun Manhas, Steve Smith, Rahul Sharma, Murali Kartik, Ashok Dinda, Ashish Nehra
Chennai Super Kings: F du Plessis, Murali Vijay, Suresh Raina, MS Dhoni, Dwayne Bravo, Albie Morkel, Ravindra Jadeja, Subramaniam Badrinath, Ravichandran Ashwin, Shadab Jakati, Doug Bollinger