The match had ended 1-1 after regulation time.
Amose had put Bengaluru DFA ahead in the 20th minute which was cancelled out by Mahesh Kumar in the 45th minute.
In the shoot-out, Clive Miranda, Kunal and Snedden scored for Goa FA.
For the Bengaluru team, only Vijay Kumar and Kaviarasan were able to convert.
Chennai FC takes on ASC, Bengaluru, in the second semi-final tomorrow.