Emenike, who plays for Fenerbahce in Turkey, tied the score in the 67th minute at Addis Ababa and converted a penalty kick in the 90th. Behailu Assefa had put the hosts ahead in the 57th.
The second leg of the total-goals series is at Calabar, Nigeria, on Nov. 16.
In Sunday's other game, Samuel Eto'o ended his brief international retirement and captained Cameroon in a 0-0 draw at Tunisia. Eto'o started in Rades after being convinced by Cameroon President Paul Biya to rejoin the squad.
The second leg is Nov. 17.
On Saturday, Ivory Coast beat visiting Senegal 3-1 and Burkina Faso won 3-2 at home against Algeria. Ghana hosts Egypt on Tuesday.