The 2010 and 2011 champions recorded their eighth win in 10 starts as they chased down 149 to win match 37 at the JSCA International Stadium Complex in Ranchi.
Captain Shane Watson's 51 led the Royals to 148-8 in their 20 overs but they were unable to defend their total as MS Dhoni saw CSK home with two balls to go.
Watson shared a 60-run opening partnership with Ankit Sharma (30) before becoming the first of Mohit Sharma's three victims in the 13th over.
He hit four sixes in his 36-ball innings and, although Stuart Binny hit two maximums in his 22, the lower order were unable to maintain the momentum.
|Ankit Sharma||c Dwayne Smith b Ravichandran Ashwin||30||27||111.11||4||1|
|Shane Watson||b Mohit Sharma||51||36||141.66||3||4|
|Ajinkya Rahane||run out (Brendon McCullum)||4||7||57.14||0||0|
|Karun Nair||b Samuel Badree||8||11||72.72||1||0|
|Stuart Binny||c Francois du Plessis b Ravindra Jadeja||22||17||129.41||0||2|
|Steve Smith||b Mohit Sharma||9||8||112.50||1||0|
|James Faulkner||b Ravindra Jadeja||1||4||25.00||0||0|
|Dishant Yagnik||NOT OUT||4||6||66.66||0||0|
|Rajat Bhatia||c Dwayne Smith b Mohit Sharma||7||4||175.00||1||0|
|Kevon Cooper||NOT OUT||0||0||0.00||0||0|
|EXTRAS||(w 8, b 1, lb 3)||12|
CSK lost Brendon McCullum and Suresh Raina to Sharma during the powerplay but they still managed 48 in the opening six overs.
In-form Dwayne Smith missed out on his sixth half-century of the tournament but his 44 from 35 balls took Chennai to 76-3 at halfway.
The limping Faf du Plessis made 38 before being yorked by James Faulkner, which left the Super Kings needing 28 off the final 15 balls.
Ravindra Jadeja hit a six in the penultimate over to leave 13 needed off Faulkner's final over from which Dhoni hit the second ball for six before an overthrow sealed the win.
|Dwayne Smith||c Dishant Yagnik b Kevon Cooper||44||35||125.71||5||2|
|Brendon McCullum||c Karun Nair b Ankit Sharma||6||3||200.00||0||1|
|Suresh Raina||c Rajat Bhatia b Ankit Sharma||2||3||66.66||0||0|
|Francois du Plessis||b James Faulkner||38||39||97.43||2||0|
|Ravichandran Ashwin||b Rajat Bhatia||14||16||87.50||1||0|
|MS Dhoni||NOT OUT||26||16||162.50||1||1|
|Ravindra Jadeja||NOT OUT||11||6||183.33||0||1|
|EXTRAS||(w 5, lb 3)||8|
Both teams are strongly placed to make the play-offs with Chennai facing Royal Challengers Bangalore on Sunday.