It was Choudhary who put India ahead in the 62nd minute while Chhetri (80th) doubled the lead of the visitors.
Substitute Anirudh Thapa's goal helps India salvage 1-1 draw against Nepal in international friendly
Anjan Bista had given the home team the lead in the 36th minute.
Thapa tested positive on Wednesday, a day before India lost 0-1 to Asian champions Qatar in their joint World Cup and Asian Cup qualifiers in Doha.
FIFA World Cup 2022 qualifiers: Need to focus on improving my goal conversion rate, says Anirudh Thapa
The 23-year-old is currently training with the Indian football team in Doha ahead of next month's 2022 FIFA World Cup and 2023 Asian Cup Qualifiers in Qatar.
FIFA World Cup 2022 qualifiers: Sunil Chhetri returns to squad as India football team departs for Doha
The team will have a preparatory camp inside a bio-bubble in Doha before its first match on 3 June against hosts Qatar.
Coach Igor Stimac was happy with youngsters but disappointed with result against UAE, says Anirudh Thapa
Ahead of the remaining World Cup qualifiers matches, Thapa mentioned that Stimac wanted to assess the new players’ performances in the friendlies against Oman and UAE to see who all were geared up for big games in the future.
The match saw both teams failing to convert clear-cut chances. That Odisha had three shots on target while Chennaiyin managed just two exemplified how much both sides cancelled out each other.
With their third win, Hyderabad FC moved up to sixth place with 12 points while Chennaiyin slipped to eight place following their third defeat.
ISL 2020-21: Use of foreign players in key positions hurting India’s chances of producing spine of national team
While it would remain advisable for the Indian team to be pragmatic and not get caught up in every tactical trend used abroad, identifying and developing players in key positions with an eye towards the future must be prioritised considering the current dilemma.
ISL 2020-21: Bengaluru FC beat Kerala Blasters in six-goal thriller; NorthEast United continue unbeaten run
The teams were tied 1-1 at the break with Rahul K P (17th) giving Kerala Blasters a surprise lead which was cancelled out by Cleiton Silva (29th)
ISL 2020-21: Lack of creativity hurting Kerala Blasters, Sunil Chhetri scores at last and other talking points from matchweeks 3 and 4
Here are the talking points from the third and fourth matchdays of ISL 2020-21.
ISL 2020-21: Sunil Chhetri's penalty against Chennaiyin FC powers Bengaluru FC to first win of the season
A 56th-minute penalty strike from Sunil Chhetri was the difference between the two teams as Chennaiyin suffered their first loss of the season.
ISL 2020-21: Bengaluru FC renew heated rivalry with Chennaiyin FC as Carles Cuadrat's men hunt for first win
There are problems aplenty for Bengaluru, who are struggling to find the attacking impetus that they have never been short of in the previous seasons.
The CFC coach has said that his team would play high-intensity football this season and going by the way the two-time champions started, the 'Men in Blue' will look to carry on in the same vein.
Thapa's early strike coupled with a penalty goal from Esmael Goncalves (26th) ensured that Chennaiyin began their campaign with a win.
ISL 2020-21, Chennaiyin FC preview: Defence an area of concern as Csaba Laszlo’s new-look side eyes third title
Ahead of the 2020-21 ISL season, we take a look at Chennaiyin FC's prospects, and where they could end up.
A product of the AIFF Elite Academy, Germanpreet made his professional debut in January 2015 for Goan side Dempo SC in the I-League, followed by a stint at Minerva Punjab FC in the same competition.
ISL: Chennaiyin FC confirm participation of Anirudh Thapa, nine other Indian players for 2020-21 season
Anirudh Thapa, who joined the club as an 18-year-old in 2016, is currently on a multi-year contract and is set for his fifth campaign in the Chennaiyin jersey.
Last week, the AFC postponed all the Asian qualifying matches for the 2022 World Cup to 2021 due to the ongoing pandemic, which has infected over two crore people across the globe.
Anirudh Thapa, Sandesh Jhingan good enough to play for international clubs, says India's assistant coach S Venkatesh
Jhingan is among the biggest names in Indian football at the moment, while 22-year-old Thapa has also impressed with his game, turning out for both his club Chennaiyin FC and the national team.