The Harambee Stars moved closer to securing a place at next year's continental gathering with a 3-0 home triumph over the Antelopes at the Moi International Sports Centre in Kasarani, Nairobi.
Goals from Michael Olunga, Eric Johana Omondi and Tottenham Hotspur midfielder Victor Wanyama (pen) sealed the win.
The match came four days after the Harambee Stars held the Antelopes to a scoreless draw in their first leg in Bahir Dar.
Tied on four points with Ethiopia and a point above third-placed Ghana and bottom-positioned Sierra Leone ahead of Sunday's matchday four fixture, Kenya have taken their tally to seven, having now played two games more than the Black Stars in Group F.
The standings, though, have to do with cancelled double-header between Ghana and Sierra due to the latter's recent Fifa ban from football.
With Caf ruling out rescheduling of the games, Ghana could be declared winners of the matches and handed six points, a scenario that will take the Black Stars to top of the table with nine points without having kicked a ball on matchdays three and four.
Alternatively, Sierra Leone could be completely taken out of the qualifying series, thereby leaving only three teams in the group. In the case of the latter, the results of Sierra Leone's two games played in the group thus far (against Kenya and Ethiopia) will be nullified, a situation that will also have a bearing on the outlook of the group.
Caf is expected to give a declaration on the status of the group anytime soon.
Ghana, meanwhile, return to action next month with an away trip to Ethiopia.
The top two teams in the group will qualify for Cameroon 2019.