The East African side had never defeated the West African nation at Afcon, losing twice and drawing once in the three previous games.
It was the Harambee Stars who got an early chance when Michael Olunga, who has scored two goals in the tournament already, almost capitalized on a weak back pass but his effort sailed over the bar.
Three minutes later, Philemon Otieno fouled Sadio Mane about 30 yards from the goal, but Patrick Matasi cleared the danger.
Kenya was lucky not to have conceded a penalty when captain Victor Wanyama handled the ball in the danger zone. The referee waved play-on amid protests from the Teranga Lions players who felt otherwise.
Matasi was called into action in the 22nd minute to deny Babacar Niang. The striker had danced past three Kenyan defenders, but he could not beat the custodian.
In the 26th minute, the Saint George goalkeeper once again was called into action, this time around denying Idrissa Gueye.
The best opportunity for the Senegalese came in the 29th minute when Musa Mohammed fouled Saliou Cisse in the danger zone. The referee correctly awarded them a penalty and Mane had a chance to score his first goal of the tournament. Matasi, however, guessed right to deny the Liverpool star from the spot.
At the stroke of half time, Matasi was once again called into action, this time around pushing out a well-placed header from Ismaila Sarr. Kenya were relieved to hear the half-time whistle.
Senegal started the second half from where they left, as the Harambee Stars comfortably sat back aiming at getting at least a point to advance to the knockout phase.
Saivet almost broke the Kenyan's resilience in the 52nd minute, but his ferocious rocket was well saved by the impressive Matasi.
Harambee Stars' first real chance fell to Dennis Odhiambo in the 60th minute, but the Sofapaka midfielder was denied by the Senegal custodian who managed to send the ball out for a fruitless corner.
A few moments later, The Lions of Teranga deservedly took the lead; a cross was brought in from the right by Lamine Gasama and the Kenyans failed to clear it. The ball eventually fell to Sarr whose first-time effort found the back of the net.
Mane doubled the advantage in the 70th minute; a long ball was played into the Kenyan half, Mohammed failed to clear the ball and it fell to the forward who easily beat Matasi to seal the win.
It became worse for Kenya in the 77th minute when Otieno conceded a penalty after a reckless tackle on Sarr. The Gor Mahia man received his second yellow card and was sent off. Mane beat Matasi this time, making it 3-0 to crown Senegal's thrashing of Harambee Stars.
Kenya XI: 18. Patrick Matasi, 20. Philemon Otieno, 3. Abud Omar, 2. Joseph Okumu, 5. Musa Mohamed, 21. Dennis Odhiambo, 12. Victor Wanyama, 8. Johanna Omollo, 7. Ayub Timbe
13. Eric Ouma and 14. Michael Olunga.
Subs: 1. Faruk Shikalo, 23. John Oyemba, 4. Joash Onyango, 15. David Owino, 6. Bernard Ochieng, 17. Ismael Gonzalez, 11. Francis Kahata, 10. Eric Johanna, 19. Ovella Ochieng, 16. Paul Were, 9. John Avire and 22. Masud Juma.