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The Barcelona talisman scored his 644th goal to surpass Pele as the all-time record scorer for a single club.
NorthEast have 11 points from eight games and are in fourth spot, while Odisha occupy the tenth place with just two points from seven matches.
David Williams' 33rd-minute strike proved the difference between the two sides.
Blasters have three points from six matches, while East Bengal have two points from six games. Both teams are yet to notch up a win.
Manchester City got back to winning ways with a 1-0 victory at in-form Southampton while Newcastle United were held to a 1-1 draw at home to struggling Fulham.
Messi equalled Pele's record of 643 goals for a single club on Saturday but was unable to help Barcelona beat Valencia in La Liga as they had to settle for a 2-2 home draw.
FC Goa tried their best through Igor Angulo and Ortiz to get the equaliser but Chennaiyin's defense was too tough to crack.
Both teams have conceded 10 goals from five matches.
The 40,000-capacity Al Rayyan Stadium will host seven World Cup matches up to the round of 16.
Aniket Jadhav's strike (53rs minute) was the difference between the two sides in what was the 500th game of the ISL.
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