The two countries drew 0-0 in Ethiopia last Wednesday, but Kenya took the initiative early on in Kasarani and struck through goals from Michael Olunga, Eric Johanna and captain Victor Wanyama.
Kenyan coach Sebastian Migne made only one change to the side held to a point in Bahir Dar, and Eric Ouma went close inside the opening 10 minutes when his shot flashed wide from the edge of the area.
Olunga broke the deadlock on 23 minutes after pulling away from his markers to curl home the first goal after being put through by Swedish-based midfielder Johanna.
Johanna bagged a second for Kenya four minutes later to dampen the spirits of the Ethiopians who had threatened to dominate possession with their trademark passing game.
Tottenham midfielder Wanyama put the final nail in the coffin when he scored from a penalty in the 72nd minute.
The victory took Kenya to seven points at the top of the group to bolster their chance of qualifying for a first Africa Cup of Nations in 14 years.
Kenya are scheduled to host Sierra Leone in their penultimate match in Nairobi in November.
However, the West Africans were suspended from competition by FIFA this week over government interference, and their double-header against Ghana was called off.
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