The Indian football team captain scored in the 34th minute of the Group H game at the Yangon Youth Training Centre, as Bengaluru claimed their first win of their campaign this season.
The Indian outfit could have added two more goals, but CK Vineeth and Udanta Singh were not lucky enough as they narrowly missed the targets.
Bengaluru are now placed third in the group with three points.
After an even opening 45 minutes, Bengaluru opened the scoring when Chhetri struck the ball into the back of the net from 12 yards.
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The home side pushed for the equaliser in the second half, but Yangon were unable to breach the Bengaluru backline as the I-League side held out to take full points.
The visitors went in front 11 minutes before the interval when Udanta Singh squared to Chhetri, and although the frontman mishit his left foot strike, the ball bounced past goalkeeper Vanal Hruai into the back of the net.
Benguluru FC will play their home leg match against the same opponents on April 13.