The win now keeps alive Kenya’s hopes of qualifying for the continental tournament for the first time since the country last made an appearance at the tourney in Tunisia, 2004.
Kenya controlled the game from the beginning to the end, looking threatening at the goal with every chance they got.
Michael Olunga opened the scoring for the Harambee Stars in the 23rd minute with a powerful left foot shot from just outside the box after receiving a pass from Erick Johanna.
The outstanding Johanna then extended Kenya’s lead four minutes later in the 27th minute with a beautifully curled left shot after he pounced on an outbound loose ball.
Kenya kept threatening and showing dominance over its opponents as the 60,000 capacity stadium roared wildly.
Olunga came close to extending Kenya's lead in the 54th minute but he failed to capitalize and a defensive mistake as the ball was cleared away from his foot.
But moments later, captain Victor Wanyama made it three nil from the penalty spot in the 67th minute after Johanna was brought down in the box.
Dennis Odhiambo almost made it 4-nil in the 86th minute after being set up by Ismael Gonzalez just outside the box but he flew the ball over the bar with Ethiopian custodian Samson Asefa beaten.
Olunga again missed a clear cut chance to register a brace in the 90th minute but he had a touch too many at the goal mouth and ended up putting the ball wide with a feeble touch.
The win now guarantees the Harambee Stars a cool Sh50 million that was promised by Deputy President William Ruto on Friday.
Nairobi Governor Mike Sonko also promised them an extra Sh3 million for a win over the Walyas.
The DP, who attended the game alongside other politicians including Moses Kuria and Kipchumba Murkomen, congratulated the team in a tweet.
"The boys have done it! A momentous occasion as Harambee Stars thump Ethiopia 3-0 to all but guarantee a place at 2019 Africa Cup of Nations showpiece. Tactical discipline, sterling team effort, fantastic home support and belief carry the day. Let's savour a great win," Ruto said.
Kenya will next travel to Accra Ghana to play the Black Stars before meeting Sierra Leone in March next year.
The game against the Leone Stars will, however, depend on FIFA's decision on the suspension of the team.
The Leone Stars were suspended by FIFA on October 5 due to government interference in the organisation and administration of the nation's football association.
It is unknown if Ghana will be awarded free points after their tie with Sierra Leone was cancelled by CAF following the team's suspension.
-The Star