While ATK struck in the 13th minute through a spectacular Arata Izumi volley, it was Keenan Almeida's cracking right footer that restored parity for Zico's men in the 81st minute in an ill-tempered match.
Both ATK and FC Goa now have three points from two games with a win and a draw to show for their efforts.
ATK's Baljit Sahni was shown the first red-card of the season after head butting opposition defender Gregory Arnolin bringing memories of the last season when the latter was involved in an identical incident with the then ATK striker Fikru Teferra.
While Japanese of Indian origin Arata, who has played for the Indian national team won the man of the match for his goal, the best player on the turf was FC Goa's left-half Jofre Mateu, who was like a livewire with his assists and pinpoint crosses.
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It was ATK who got the lead in the 13th minute against the run of play. Winger Javi Lara floated one from the wide right inside the box for Iain Hume. Before the Goa defence could get their shape right, Arata came from behind with reflex snap volley that beat a diving goalie Elinton Andrade.
Skipper Lucio was seen on the overlap while Jofre fed some great balls for Reinaldo and Le Moura upfront.
However Oftense Nato and Denzel Franco had a great game at the back as they foiled their bid to score in their defensive third.