The two teams were tied 1-1 at half-time.
The tournament kicked off on Saturday with Group A matches, where host Tanzania lost 1-0 to Zambia and Burundi defeated Somalia 2-0.
In Group B matches played yesterday, Zanzibar shocked Sudan 2-0 and Rwanda edged past a domestic league-based Ivory Coast team 2-1.
EthiopiaÃ¢â‚¬â„¢s next game will be against Kenya on Thursday and against Malawi on Saturday.
In this yearÃ¢â‚¬â„¢s tournament, there are 12 teams drawn in three groups of four, with the top two sides in each pool qualifying for the quarter-finals, along with the two best third-place finishers.
2010 CECAFA Challenge Cup groups:
Group A: Tanzania, Zambia, Burundi, Somalia
Burundi 2 – 0 Somalia
Tanzania 0 – 1 Zambia
Group B: Rwanda, Ivory Coast, Sudan, Zambia
Sudan 0 – 2 Zanzibar
Rwanda 2 – 1 CÃƒÂ´te d’Ivoire
GROUP C: Uganda, Kenya, Ethiopia, Malawi
Ethiopia 1 – 2 Uganda
Kenya vs Malawi 2-3