Miya scored twice in the first half, the first on 10 minutes from a Erisa Sekisambu pass, before rounding Zanzibar goalie Ali Mwadini.
His second came seven minutes later from the spot goal come in from a spot kick after Sekisambu was fouled by Mwadini, who was sent off. Miya stepped up to place the ball beyond substitute goalkeeper Mohammed Abdurahman.
Zanzibar on the other side depended on Yanga SC striker Simeon Mateo but the youngster was well checked by the defensive duo of Kasagga and Jjuuko Morushid as Alitho James kept the watch from the post.
Sekisambu, deployed on the right wing scored the third three minutes after the break with a perfect strike from a Muzamiru Mutyaba assist.
Zanzibar handled by Hamed Suleiman suffered another blow on 73 minutes when Yahya Mudathir was shown a straight red card for a flying tackle on Sekisambu.
Ceaser Okhuti put the icing on the cake on 78 minutes. Debutant Nelson Senkatuka and fellow substitute Frank Kalanda combined well to put the Express FC man through, who unleashed a left-footed shot into the back of the net.
The win takes Uganda to the top of the group on three points via superior goals. Burundi and Kenya have three points each.
Meanwhile, Tanzania registered their second victory at the tournament after they edged out Rwanda 2-1 in Group A.
Tanzania’s Khamis Juma scored a wonder free-kick in the 28th minute after Jean-Baptiste Mugiraneza fouled John Bocco to give the Simbas a first half lead.
The Rwandese maintained the pressure going into the second half but forgot to cover their back and this allowed Simon Msuva to score Tanzania`s second in the 78th minute.
Jacques Tuyisenge pulled a late consolation in the in the dying minutes of the game.
Tanzania lead Group A with six points and Rwanda on three after two games each.
Tanzania 2-1 Rwanda
Uganda 4-0 Zanzibar