South African Sameehg Doutie put ATK ahead as early in the sixth minute but they failed to make much headway as the Goans bounced back riding on a spot kick from Joffre Mateu in the 76th minute.
Both teams were reduced to 10 players with ATK receiving as many as three yellow cards and one red, while FC Goa had a share of four yellow cards and one red in the hard-fought match at the Rabindra Sarobar Stadium.
ATK now have one win and three draws to be on the third place with six points.
A clinical strike from Sameehg Doutie put ATK ahead in the sixth minute, a goal that resulted from the freekick after Iain Hume was brought down by Raju Gaikwad. Javier Lara put the ball into the far post from the freekick where Hume headed it in the danger area before being cleared by Gaikwad.
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But the header went straight to Doutie on the edge of the box as the South African welcomed it by blasting his volley past a diving Subhasish Roy Chowdhury to his left.
The Goans restored parity after ATK conceded a penalty through Borja Fernandez's handball as the captain was seen hit on his arm trying to chest the ball.
ATK were reduced to 10 players in the 52nd minute when
their Scottish midfielder Stephen Pearson was sent off for a rash tackle on Trindade Goncalves.
Goans' turn came in the 60th minute when the Sanjay Balmuchu was sent off after being shown a second yellow for a foul on Prabir Das.
That the Gaurs dominated the possession in the first 45 minutes without being able to convert a single opportunity summed up how their attack kept Majumder busy under the bar.
First it was Trindade Goncalves who tested Majumder with a one-on-one in the 16th minute but the ATK goalkeeper stood tall making an excellent save.
In the 38th minute, Robin Singh's right-footer from the edge of the box was on target but Majumder dived full length to his right to make a fingertip save.
The other two matches were won by Atletico de Kolkata, including a 4-0 in their last meeting in Kolkata.