Fahad Aziz Bayo scored the lone goal for Uganda in the 41st minute following a goal mouth melee to send Uganda atop of group E.
The Cranes have not conceded a goal in their 3 matches so far and they await the result between Kenya and Mali to see whether they keep their place at the top.
Rwanda’s Jacques Tuyisenge and York Rafael missed valuable opportunities for Rwanda in the early minutes of the game
Haruna Niyonzima could have found an equaliser for the hosts but Charles Lukwago was equal to his close range shot.
In the 59th minute , Steven Mukwala wasted a glorious opportunity to extend Uganda’s lead when he poorly connected with Isaac Muleme’s perfectly weighed cross.
Micho made a double substitution in the 64th minute by introducing Julius Poloto and Aziz Kayondo for Bobosi Byaruhanga and Isaac Muleme respectively.
Rwanda also made a double change. Dennis Rukundo and Muhadjir Hakizimana replace Fitina Omberanga and Haruna Niyonzima
Rwothomio Cromwell came on for the goal scorer Fahad Bayo in the 72nd minute.
Yunus Sentamu and Martin Kizza also came on for Mukwala and Moses Waiswa with two minutes to go.
It is Uganda’s only second away win in World cup qualifiers, the first came in 2015 against Togo.
Kenya and Mali will face off later in Nairobi in another group E match