Diaby, who is on loan from Lille OSC at Belgian outfit, Royal Mouscron-Péruwelz, netted shortly after the half-hour mark to set Mali on their way.
Yatabaré added the second on the hour mark as Mali saw out their second win from three group B outings.
The win took The Eagles to six points, three clear of Malawi, who were beaten 2-0 by Algeria in Blantyre, earlier on Saturday.
Algeria top group B with nine points.
The defeat leaves Ethiopia rooted to the bottom of group B with no points. Ethiopia were defeated by Algeria and then Malawi, before Mali piled further misery on coach Mariano Barreto and his troops.