The Islanders got the winner on the hour mark courtesy Rasolofonirina for their second successive win of the campaign.
The host got off on a positive note but the Amavubi backline of Fitina Ombalenga, Salomon Nirisarike, Abdul Rwatubyaye and Abouba Sibomana defended well.
‘Les Dodos’ had two good opportunities to kill the game in first half but found Rwanda goalkeeper Eric ‘Bakame’ Ndayishimiye difficult to beat.
Rwanda had three shots on target through Jean-Claude Iranzi, Elias Uzamukunda and Jean Baptiste Mugiraneza but failed to hit the back of the net.
The homers relied on counterattacks with striker Kevin Bru leading the onslaught and even hitting the post before the break.
Rwanda responded and a three-man move involving Jean-Baptiste Mugiraneza, Haruna Niyonzima and Iranzi had Mugiraneza at the end but his shot came off the post.
Midway in the second half, Rasolofonirina scored the lone goal that separated the two sides.
Rwanda will host the reverse three days later in Kigali, and need nothing short of the maximum points to bounce back into contention.