Chasing 140 for victory, the Knight Riders finished the task with two balls to spare, with Gambhir leading the way with a 52-ball 63 at the M A Chidambaram Stadium.
Gambhir struck six fours and a six.
Needing six runs in the last over bowled by Ravichandran Ashwin, newcomer Debabrata Das (11 not out) pulled it off for KKR by hitting a boundary after Yusuf Pathan got out to an irresponsible shot.
The Knight Riders lost opener Brendon McCullum early, but Gambhir held his ground and, in the company of in-form Jacques Kallis (26 off 31 balls), stabilised the innings.
Introduced in the third over, Ashwin foxed McCullum with the carrom-ball as the batsman scooped it to mid-off.
But success was hard to come by thereafter for the Super Kings as Gambhir and Kallis added 70 runs for the second wicket, the partnership ending after the latter edged Dwayne Bravo to CSK skipper Mahendra Singh Dhoni.
But before that, as they were not chasing an imposing total, both the batsmen seemed content to play the ball on merit, but the loose ones were never really wasted.
The Super Kings bowlers were never allowed to settle into any sort of rhythm by Gambhir and Kallis who displayed good footwork on what was not the ideal track for batting.
After Kallis heaved Ashwin over deep square-leg for a six, Gambhir went down the pitch to deposit Shadab Jakati over long-on for a maximum.
However, Dhoni’s move to bring back Bravo to bowl the 13th over, paid immediate dividend as that resulted in the dismissal of Kallis.
Chennai tried to apply pressure on KKR, but Gambhir was equal to the task as he took his team to within sniffing distance of victory.
Earlier, Kallis led a disciplined bowling effort with two important wickets as the Knight Riders restricted the Super Kings to a modest total.
Kallis took the wickets of Suresh Raina, who top-scored for the hosts with a 34-ball 44, and West Indian hard-hitter Dwayne Bravo, to finish with 2/21.
Dhoni remained unbeaten on 34 off 30 balls.
Opting to bat after winning the toss, Super Kings were never allowed to get off the hook by the KKR bowlers.
The Super Kings were off to an inauspicious start, losing big-hitting opener Faf du Plessis in the second over of the match to Brett Lee, who induced an edge that was taken by wicketkeeper Brendon McCullum.
A few overs later, dangerman Michael Hussey was run out by the Lee-McCullum combo, to leave the hosts in some sort of trouble at 32 for two in the fifth over.
Raina, along with Bravo, tried to take the Super Kings to a comfortable situation, but the West Indian holed out to long-on fielder Iqbal Abdulla off the bowling of Kallis after being involved in a 42-run stand for the third wicket.
With his team struggling to dominate the opposition, Dhoni strode to the crease, and responded to the situation by running a few quick singles and hitting the occasional boundaries.
Having taken the wicket of Bravo, Kallis struck once again, sending back Raina. After a fumble, Yusuf Pathan managed to hold on to the catch at midwicket after Raina played it high in the air.
During his stay at the wicket, Raina entertained the partisan crowd with some fluent hits to the fence.
Chennai Super Kings: Faf du Plessis, Subramaniam Badrinath, Michael Hussey, Suresh Raina, Ravindra Jadeja, MS Dhoni, Dwayne Bravo, Albie Morkel, Ravichandran Ashwin, Shadab Jakati, Yo Mahesh
Kolkata Knight Riders: Brendon McCullum, Gautam Gambhir, Jacques Kallis, Yusuf Pathan, Manoj Tiwary, Debabrata Das, Laxmi Shukla, Brett Lee, Rajat Bhatia, Sunil Narine, Iqbal Abdulla