The Tata boys continued their dominance and scored a brace in the last three minutes to seal East Bengal's fate.
TFA seized the lead in the 87th minute when Robin Singh's cross was headed into the net by Irfan Khan.
A minute from close, Jagtar set up Robin Singh, who found the net.
TFA, who drew with United Sporting Club in their lung-opener, now lead the group with four points. Only one team will reach the semis from the group.
United, who take on East Bengal in their last league match Sunday, not only have to win, but also better the TFA boys in goal difference to make it to the last four.