Chennai Super Kings choked in the end despite cruising at the half-way stage in their 168-run chase, ending up with a disappointing 157 for five.
Shane Watson played a lone hand of 50 while the rest failed to fire and thus, went down by 10 runs in Abu Dhabi.
Kolkata Knight Riders came back strongly in the match through Andre Russell (1/18), Kamlesh Nagarkoti (1/21), Varun Chakravarthy (1/28) and Sunil Narine (1/31) to win their first match CSK in 2 seasons.
Chennai Super Kings staged a remarkable comeback after opener Rahul Tripathi's 51-ball 81 to bowl out Kolkata Knight Riders for 167 in the Indian Premier League here on Wednesday.
Batting first, KKR lost three wickets in the last over with Dwayne Bravo removing two of them.
Bravo, a CSK veteran, celebrated his 37th birthday by returning impressive figures of 3/37 in his quota of four overs.
Tripathi enjoyed his promotion to the top with an excellent fifty but Chennai Super Kings bowlers applied the brakes to bundle out Kolkata Knight Riders.
Tripathi picked up from where he left off against Delhi Capitals and raced to his fifth IPL fifty in 31 balls to give KKR a solid foundation after Dinesh Karthik called it right at the toss. At 93 for two at the midway stage, KKR looked set for a big score but Bravo struck after that.
Leg-spinner Karn Sharma (2/25), Shradul Thakur (2/28), Sam Curran (2/26) claimed two wickets each as the Mahendra Singh Dhoni-led side bounced back in the back 10 by taking eight wickets while giving away just 74 runs.
Dhoni picked up four catches, the last one being his best effort.
On a Sheikh Zayed Stadium pitch that seemed to slow down, Tripathi played a risk-free knock and maintained a healthy run-rate.
Karthik made a baffling decision by sending Sunil Narine ahead of their best batsman, Eoin Morgan, at No. 4.
However, Narine did his job with a nine-ball 17 before being dismissed by an excellent combined effort by a diving Ravindra Jadeja and Faf du Plessis.
Morgan started with a classical cover drive boundary but Curran cut short the with a bouncer that climbed in and took a faint edge behind the stumps.
Thakur, who had given the first breakthrough by dismissing an in-form Shubman Gill (11), claimed the big wicket of Andre Russell with a cross-seam short delivery as the KKR dazzler struggled to get going.