Rwanda shocked Libya in the second leg of their 2015 Africa Cup of Nations qualifier, winning 3-0 at home to progress to the next round.
The sides had been locked at 0-0 after the first game but a hat-trick from Dady Birori saw Rwanda comfortably home in Kigali.
The Wasps, playing in their first game under new coach Stephen Constantine, are 27 places below Libya in the Confederation of African Football rankings.
Rwanda will next face either Namibia or Congo.
Earlier, Uganda squeezed past Madagascar with a 1-0 second-leg win that put them through on away goals after the tie ended 2-2 on aggregate.
Geoffrey Massa struck for the Cranes after only 13 minutes but Uganda were unable to find their way through again and had to come through a tense finish in Kampala to book their place in the next round.
Sierra Leone booked their place in the second round with a 1-0 over Swaziland in Freetown on Saturday. Skipper Umaru Bangura scored from the penalty spot in the 65th minute to give Sierra Leone a 2-1 aggregate victory.
On Friday, Mozambique and Kenya became the first teams to reach the final qualifying round after playing their second legs on Friday.
With a 5-0 lead over South Sudan from their first encounter, Mozambique were huge favourites to progress. South Sudan, however, managed to salvage some pride at least, by holding their opponents to a 0-0 draw at home.
Kenya made it through after drawing 1-1 away to Comoros Islands, giving them a 2-1 win on aggregate.
Malawi scraped through on away goals after crumbling 3-1 in Chad with Rodrique Ninga bagging a brace for the home side and Casimir Rodrigues also scoring. The tie-deciding goal came late in the second half from Malawian Robin Ngalande, who was on the books of Atletico Madrid as a youth.
Having been held to a 0-0 draw in the first leg, Central African Republic slumped 3-1 away to Guinea-Bissau in Bissau. A Cicero Semedo brace plus one from Bacar Balde within 26 minutes thrilled the home crowd. The visitors could only manage a Josue Balamandji second-half consolation.