Mudathir Yahya, Mohamed Juma and Kassim Khamis netted the three goals for the Isles outfit and handed Rwanda the second consecutive defeat in the event.
Midfielder, Muhajir Hakiziman, scored what turned out to be a consolation for Rwanda, who had suffered a 2-0 loss to Kenya in the opening match.
In the yesterday match, the teams attacked in turns right from the start and there were a couple of good chances for either side.
Zanzibar Heroes' left fullback, Mwinyi Haji, attempted a dipping shot from the left on the 22nd minute and forced Rwanda's keeper to tip the ball over the crossbar.
Rwanda had earlier wasted two good chances on the 16th minute, in which the outfit's forwards headed over from inside Zanzibar Heroes' box.
Zanzibar Heroes' midfielder, Mudathir Yahya, tested Rwanda's keeper with a right foot shot from almost 30 meters on the 31st minute, only to see the attempt go across the face of the goal.
Yahya put Zanzibar Heroes 1-0 up on the 35th minute after heading in a well taken cross by Haji from the left.
Zanzibar Heroes pushed forward on the 37th minute and a weak right foot effort by Yahya from inside Rwanda's box was easily saved by the latter's keeper.
Midfielder Hakizimana, drilled in an equalizer for Rwanda two minutes into the second half.
Hakizimana had earlier picked his team mate with a lob and the latter then set up the former.
Zanzibar Heroes restored their lead eight minutes later through Mohamed Juma, who beat Rwanda with a left foot shot from outside the latter's penalty area.
Zanzibar Heroes were under pressure on two occasions in the latter stages and the outfit needed good goalkeeping by its keeper to keep Rwanda at bay.
Second half substitute, Kassim Khamis, scored the third for Zanzibar Heroes on the 86th minute, beating Rwanda's keeper with a left foot effort from inside the area after he had been set up by his team mate.
Zanzibar Heroes have, therefore, boosted their chances of progressing to the next stage of the event.
They are then expected to face fellows, Kilimanjaro Stars, at the same venue tomorrow. Kilimanjaro Stars started their campaign in the event with a 0-0 draw with Libya last weekend.
Kilimanjaro Stars’ head coach, Ammy Ninje, said he is expected to work on his side’s weaknesses that were in view in the game against Libya.