The home team started the match on a bright note making key inroads within the initial minutes but both Allan Wanga and David Gateri's chances went wide from close range.
Gateri should however have done it in the fourth minute from an Edwin Lavatsa cross from the right but the South Africa based midfielder took long to be in position with the ball going wide for a goal kick.
Thika United midfielder Francis Kahata then ran through the right flank but his cross was too weak in the 20th minute and the ball again went inches wide.
Ethiopia had their chances on goal as their fast paced players forced Harambee Stars players to commit fouls with David Owino and Aboud Omar getting cautions from rough tackles in the first half.
Musa Mohammed has a chance to set up Allan Wanga towards the dying minutes of the first half but the ball was snatched from his feet by Ethiopia's skipper with Wanga waiting in the box.
The second half was a nail biting encounter as both sides went for the offensive early enough with both keepers being kept busy between the post for the entire time.
Ethiopia had the chance to take the lead through a curled in freekick by Yousuf Yassin but Duncan Ochieng' was at hand to save the situation.
Stars then attacked with Lavatsa earning Stars a freekick at the edge of the area after being fouled by Thok James but the freekick by Kahata could not be put beck to play by Atudo who placed it over the net.
South Africa based David Gateri then missed what many viewed as golden chance after being released by Aboud Omar and Lavatsa tripping with the defender already beaten and in the right shooting position.
The player was substituted moments later with the golden boot winner Jacob Keli taking his place at the front of the team's attack but the Ethiopians kept up their attacks.
Lavatsa and Kahata then engaged in a lovely 1-2 in attack but the later's pass was too powerful for Lavatsa who had already waiting in the box. Experienced striker Yonatan Kebede did not time to get a shot on target after coming on after being tightly marked.
This result leaves Zanzibar atop of Group 'A' after winning in the tournament opener against South Sudan while the latter is sitted at the bottom of the standings.
Kenya and Ethiopia are tied at a point after the draw.