Esther Sunday scored Falcons' first goal in the 26th minute when she connected a cross and beat goalkeeper Dagmawet Bekele with a left foot.
The African champions who came back stronger in the second half increased the tally in the 64th minute through Stella Mbachu.
Perpetua Nkwocha, two minutes later outpaced a defender and the onrushing goalkeeper Bekele before she tapped the ball into the yawning net.
Ngozi Okobi, would have made it four during the added time as she failed to beat the Ethiopian goalkeeper on one to one situation, after two other goals scored by the Falcons were overruled.
The Falcons with six points in the kitty need only a draw in their last game billed for Sunday in Malabo against Cote d'Ivoire.
Meanwhile, Cameroun's Lionesses also yesterday dumped Cote d'Ivoire 4-1 in another group B game leaving both sides with three points each.