The two-time champions, who had started the season with two wins, could not get the better of a struggling Kolkata side despite having the better of the exchanges through the night.
Lallianzuala Chhangte (41st) broke the deadlock with a powerful shot from a defensive error but VP Suhair (50th) restored parity before Chennaiyin captain Anirudh Thapa (74th) sealed the deal with a fine strike
Vladimir Koman (66th minute) scored from the spot to give Chennaiyin a crucial lead, eventually sealing all three points
Apart from the new coach Bozidar Bandovic, Chennaiyin have also signed five new foreign players.
ISL 2021-22: Check out Indian Super League (ISL) match start date and time, schedule, latest news and updates, live telecast channels and many more.
ISL 2021-22: Eight weeks pre-season enough to prepare team for season, says Chennaiyin coach Bandovic
Chennaiyin FC finished eighth last season and Bandovic said they will do better in ISL 2021-22.
Koman made his senior national team debut for Hungary in 2010 and went on to play 36 matches, netting seven goals. He was a vital cog in the country's third-place finish in the 2009 FIFA U-20 World Cup and emerged as the second-highest scorer with five goals.
Lukasz, who has 49 goals and 21 assists in his 200-plus club appearances so far in his career, will be eager to make his mark in his debut ISL season.
Davinder missed the last three editions of the ISL with a knee injury suffered ahead of the 2018-19 campaign.
Borysiuk will be joining Chennaiyin following a two-year spell at Polish outfit Jagiellonia Bialystok.
CFC co-owner Vita Dani said the partnership with Nivia would help widen reach across Tamil Nadu.
The forward becomes the first Kyrgyz player to feature in India's premier football league.
The 32-year old Brazilian, who captained CFC in 2020-21, was ruled out for almost half the season after suffering an ankle injury during a game against ATK Mohun Bagan.
ISL clubs will now have to field a minimum of seven Indian footballers at one time, from the previous six.
Bandovic, who joins the club after a successful stint in Thailand with Buriram United, takes over from Czaba Laszlo, who was at the helm in the previous season.
Das joins CFC after a season-long stint with SC East Bengal and is currently the second highest capped player in the ISL with 107 appearances till date, a press release said.
A tough and resilient presence on the right wing, the 30-year-old Reagan had joined Chennaiyin from NorthEast United ahead of the 2020-21 season in Goa.
The CFC Foundation has joined hands with the ISL club's official associate sponsor ACKO Insurance in supporting Akshaya Patra Foundation's initiative to distribute the dry ration kits.
Edwin, who joined Chennaiyin ahead of the 2019-20 ISL campaign, played a starring role in defence and midfield in his debut season.
ISL 2020-21: From Kerala Blasters' Sahal Abdul Samad to ATK Mohun Bagan's Manvir Singh, Indians who impressed in league stage
As the curtains are drawn on the league phase of the 2020-21 ISL season, the time is perhaps ripe to delve deeper into the standout Indian performers from each team and the impact they had on their respective sides’ journeys.