Mali have registered a second straight 2022 World Cup qualifying win after condemning Harambee Stars to a 1-0 defeat at Nyayo Stadium on Sunday.
After helping Mali to register a 5-0 win in the first leg in Morocco on Thursday, Kone found the back of the net 10 minutes into the second half with their first shot on target.
Mali almost took the lead in the second minute when Richard Odada lost the ball in the midfield that was picked up by Moussa Djenepo, but Joseph Okumu was lurking around to clear the danger and save Kenya from going down early in the first half.
Kone, who registered a hat-trick in the first leg, almost got Mali an opener in the fourth minute, but Odada did well to block him as he was about to step into Kenya's isolated penalty area.
Mali's Ibrahim Mounkoro did well to stop Michael Olunga's effort in the seventh minute when Duke Abuya did well to outmanoeuvre opponents. He laid the ball on the path of the Kenyan captain whose effort was magnificently stopped.
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Mounkoro was alert again in the 15th minute when he stopped Aboud Omar's close-range free-kick. Moussa Doumbia fouled Abdallah Hassan along the right-wing resulting in the free-kick that Kenya's full-back unsuccessfully took as he aimed for the top corner.
Muchiri failed to beat Mounkoro in the 20th minute after he was sent through on goal by Olunga. The Tusker midfielder tried to find the far corner, but the TP Mazembe goalkeeper stretched far enough to punch the ball back into play.
Kenya lost a clear opportunity in the 29th minute when Hassan went past Falaye Sacko on the right-wing but - while inside the box - he decided to find the right corner instead of passing the ball to Olunga, who was unmarked on the other end.
Mali would have grabbed the lead in the 43rd minute when Brian Bwire was caught off guard by a Kone diving header that hit the crossbar and went back into play before the Tusker goalkeeper composed himself and collected it quickly.
Hamari Traore conceded a 50th-minute foul on Olunga at the edge of the box, but Muchiri's effort was punched away by Mounkoro, who was at this moment the busier of the two goalkeepers.
Kone put Mali in front in the 55th minute with a clinical left-foot finish. Adama Traore, after speeding down the left-wing, picked up the goalscorer who fired into the top corner after a beautiful turn in a crowded penalty area.
Kenya's call for a penalty in the 82nd minute was dismissed after Henry Meja - who came in for Muchiri two minutes earlier - fired a shot that looked to have hit the hand of Sacko in the box.
Harambee Stars were not as adventurous in the second half as they were in the first and that allowed the West Africans a chance to attack, score and grab three points to remain top of Group E.
Kenya will face Rwanda at home before a game against Uganda in Kampala in the remaining qualifying fixtures.