The Desert Warriors came from behind to secure their third victory in four games in the qualifiers.
Uganda took an early lead through Zamalek midfielder Travis Mutyaba's goal in the ninth minute.
However, Houssem Aouar equalized for Algeria just one minute into the second half.
Two minutes before the hour mark, Saïd Benrahma scored the winning goal, propelling his team to the top of Group G with nine points.
Botswana, who defeated Somalia 3-1 earlier on Monday, currently sit in second place with six points from four games.
Guinea and Mozambique also have six points each and are set to face off in Morocco, where Guinea plays their home games, later on Monday.
In Group C, Nigeria, the runners-up of the Africa Cup of Nations, continued to struggle in the World Cup qualifiers with a 2-1 loss to Benin on Monday.
Despite Raphael Onyedika scoring in the 27th minute, the Super Eagles conceded two goals in the 37th and 45th minutes, courtesy of Jodel Dossou and Steve Mounie, respectively.
Nigeria had previously been held to a 1-1 draw at home by South Africa on Friday. With three points from four games, the Super Eagles currently occupy fifth place in the six-team group.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)
Short link: