Raina anchored the innings with his 50-ball knock and skipper Dhoni provided the late fireworks as Chennai overcame a slow start to post a challenging 164 for three.
Paceman Mohit Sharma then rocked the Pune top-order in a fiery spell in which he dismissed Aaron Finch (15), T Suman (0) and Yuvraj Singh (5) from which the hosts never recovered and managed just 127 for nine.
Finch was caught behind and Suman was trapped in successive balls in Mohit's first over. He returned to scalp Yuvraj. Raina's electric fielding resulted in run out of Robin Uthappa (10) which left the hosts reeling at 43 for four inside fifth over.
As if that was not enough, Luke Wright was run out in an unfortunate manner when Steve Smith played a solid straight drive but the ball touched Albie Morkel's foot before hitting the stumps and Wright was caught out of crease.
A terrible mix up meant that Abhihek Nayar too was runout. Smith handed back a simple catch to Ravindra Jadeja a few overs later and with that wicket Pune were on their way to their eighth defeat from 10 matches.
Earlier, Raina showed a lot of maturity while batting as he did the spade work along with S Badrinath (34) while Dhoni batted amazingly in his side's remarkable recovery later on.
After losing Michael Hussey (5) and Wriddhiman Sahara (13) early, Raina and Badrinath steadied the ship with a 75-run stand for the third wicket.
But it was 61-run unbeaten partnership between Raina and Dhoni for the fourth wicket that spoilt all the good work Pune bowlers had done earlier.
It rained fours and sixes when Dhoni batted as Chennai collected 50 runs in the last four overs. Dhoni punished hapless bowlers with seven boundaries including three sixes, the last one coming off the last ball.
Raina helped himself with five fours and a six.