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City won the two-legged tie 5-2 after a 2-0 win in the second.
Chhangte scored two of City three late goals in a 3-2 win at Fatorda.
While Goa's first goal by Noah Sadaoui was a product of a proper team effort, the other one by Brandon Fernandes was one of the most sensational solo strikes of the season.
The Gaurs round off their league campaign with 45 points from 22 matches. They are thus level on points with Mohun Bagan Super Giant who play Mumbai City FC on Monday.
Chennaiyin FC are peaking at the right time and they now stand at 27 points from 21 matches.
Noah’s treble was complemented with a late strike by Spanish striker Carlos Martinez as Goa moved to 39 points in the standings, equalling their nearest competitors Odisha FC and the Mohun Bagan Super Giant.
Goa won 2-1 against ten-man Bengaluru at the Fatorda Stadium.
The match ended 3-3 after Carlos Martinez scored in the 84th minute.
Goa won 1-0 with Sadaoui's 42nd minute goal proving to be the difference.
The West Coast Derby has often produced fireworks, but FC Goa has not won against Mumbai City FC in the ISL in over four years.