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.
Goa were keen to impose themselves on the Highlanders and came close in the fifth minute. Fernandes played a long diagonal pass from inside his own half to find Mendoza on the flank, but the latter shot straight at keeper Subhasish Chowdhury.
For Bengaluru, Cleiton Silva (27') and Juanan Gonzalez (57') scored and till the hour mark,
Both teams failed to create clear-cut chances in the first-half, staying defensively organised. As a result, no shots on target were registered. But it was Goa, who appeared more threatening.
SC East Bengal played most part of the second half with 10 men after captain Daniel Fox was sent off in the 56th minute.
FC Goa clinched their first win of the ongoing Indian Super League season as they beat Kerala Blasters 3-1 at the Fatorda Stadium, in Margao, on Sunday.