The Desert Foxes are now level with Senegal at the top of Group C, after two first half goals from Baghdad Bounedjah and Riyad Mahrez.
Algeria came out strong right from the off as Bounedjah and Youcef Belaili looked for the opening goal of the match.
It was then Al Sadd’s forward Bounedjah who scored from the penalty spot 34 minutes in, following great individual play from Youcef Atal as he dribbled into the box before being fouled.
Mahrez then doubled the score line just before the break, as man of the match Ismael Bennacer drilled a dangerous ball into the box and the Manchester City winger then saw his deflected shot go in.
Algeria continued the momentum into the second half, coming close twice, Bounedjah tested the keeper as well as Belaili who saw his shot straight at the Kenya stopper Patrick Matasi after being played through by Sofiane Feghouli.
Kenya improved as time passed, but failed to register a shot on target as Aissa Mandi did well to time his tackle to deny Michael Olunga’s chance late on.
Algeria will now face Senegal for the top spot in group C on Thursday.
Algeria XI: M’bolhi, Atal, Mandi, Benlamri, Bensebaini, Guédioura (71’ Abeid), Mahrez, Feghouli, Bennacer, Belaïli (74’ Brahimi), Bounedjah (81’ Delort)
Subs: Doukha, Tahrat, Halliche, Fares, Ounas, Slimani, Boudaoui, Oukidja, Zeffane, Abeid
Kenya XI: Matasi, Otieno, kumu, Mohammed, Omar Khamis, Wanyama, Odhiambo (89’ Athuman), Omondi (72’ Omolo), Kahata (45’ Ouma), Masika, Olunga
Subs: Shikalo, Onyango, Ochieng, Avire, Owino Odhiambo, Were, Juma, Ochieng, Oyemba