Pre-tournament favourites Ivory Coast were held to a goalless draw by neighbours Burkina Faso in Monday's only African Nations Cup Group B game.
Dutch goalscorer Robin van Persie said his team was rewarded for hard work.
A brace from Fran Sandaza (58, 63') and goals from Aridane Santana (86') and Joao Victor (90') helped Hyderabad climb to third on the league table.
Khalid Jamil also created history by becoming the first Indian to coach three or more league games and guide a side to the playoffs.
Goa were reduced to 10 men in the second half after Ivan Gonzalez received marching orders following two yellow cards within a span of seconds.
FC Goa took the lead through Igor Angulo (20th minute) and Redeem Tlang (23rd) before Suresh Wangjam (33rd) reduced Bengaluru's deficit.
Adam Le Fondre put Sergio Lobera's men further ahead in the 59th minute as Hyderabad tasted their first defeat of the season.
Fowler, according to the committee, did not respond and said that he 'never intended to make any racist remarks and no malice was ever intended.'