Kenya led 2-0 in the first half through goals from Johanna Omollo and Ayub Timbe before Harun Shakava made it 3-0 in the 50th minute.
After the third goal Kenya suffered two lapses in defence that almost allowed the Mauritians back into the game as they got goals in the 66th and 78th minute through Andy Sophie (penalty) and Jonathan Bru.
However, late goals by Johanna Omollo (83rd minute) and Michael Olunga (87th) thwarted any hopes of the hosts staging a comeback as Kenya marched to a memorable away win.
The win puts Kenya on course to progressing to the second round qualifiers where Harambee Stars will face Cape Verde.
Radiojambo.co.ke caught up with former Harambee Stars coach Jacob Ghost Mulee after his breakfast show on Radio Jambo and he had the following to share about Kenya's win, Bobby Williamson's tactics and the threat posed by Cape Verde.