Rwanda moved top of Group K after matchday two games, following their hard-fought 2-1 win over Cape Verde away in Praia on Tuesday.
The Amavubi Stars had to come from a goal down to earn victory and make it two wins in as many games.
Benchimol had given Cape Verde the lead after five minutes but Rwanda were able to level matters at the stroke of halftime through Claude Niyomugabo.
Elie Iradukunda Tatou then got the winner seven minutes after recess and the visitors had to defend resiliently to take maximum points.
Victory takes Rwanda top of Group K on six points, following their 3-1 win against Liberia on matchday one.
