Unfurl a map and, despite the rather large clue in the country's name, many people wouldn't be able to point to the Central African Republic. And yet this is the land of the most successful national team on the planet. Sort of.

CAR have zoomed up 90 places in the Fifa world ranking since the last World Cup, making them the highest risers in the world. Their unexpected ascent owed much to one of the greatest recent shocks in international football: if the 0-0 draw that Les Fauves earned in Morocco in their opening match of qualification for the 2012 Africa Cup of Nations came as a surprise, their next result was astonishing – in October they hosted Algeria, who only a few months previously had held England to a draw at the World Cup and triumphed 2-0. It was their first senior competitive victory since 1973. And it was no fluke, as CAR overran the visitors for long periods. With four points from two games Les Fauves go to Tanzania this weekend knowing that a win will give them an excellent chance of qualifying for a major tournament for the first time.

The buildup has not been promising. It never is for CAR. One of the reasons they were ranked 202 in the world in August (now they are 112th, four places above Wales) is that they seldom get to play. Habitually eliminated in – or withdrawn from – the preliminary qualification rounds for major tournaments, they do not have the money to play friendlies, meaning they had contested only one full senior match in the three years prior to the draw with Morocco.

The handful of domestic-based players in their team do at least take part in the annual CEMAC Cup, a competition for amateur players from the six countries that comprise the Economic and Monetary Community of Central Africa. Cameroon normally win that but in 2009 CAR prevailed for the first time, beating Equatorial Guinea 3-0 in the final. In 2010 they finished third. Many of the players who competed in those campaigns make up the current team but none had made much of an impression on the wider world, nor even on Jules Accorsi, the 73-year-old Frenchman who admitted to having "no idea" about the players he was inheriting when he was appointed CAR manager last summer.

The jubilation that followed their victory over Algeria has not translated into improved working conditions for the CAR team. They still do not have a kit sponsor. They still can't arrange international friendlies – whereas Tanzania have played nine friendlies in the past six months, Les Fauves' only match since the Algeria win was last week's 1-0 win over local club AS Tempête Mocaf. The FA continually complains that neither the government nor local businesses seem interested in supporting the team, although this month the government did at least manage to cough up the wages owed to Accorsi, thereby preventing the manager from walking out just before what is perhaps the biggest match in the history of the Central African Republic.

Accorsi has selected a 25-man squad consisting of a handful of players from domestic clubs and others from small European clubs such as Kecskemet in Hungary and Zulte Waregem in Belgium. The forwards Hilaire Momi of Cameroonian champions Coton Sport Garoua and Charly Dopekoulouyen of Raja Casablanca are perhaps the team's best-known players. Exactly. "Our biggest strength is our mentality," Accorsi told Radio France Internationale. "This is a group of players who want to prove themselves. Most of them don't play in big clubs, even the ones in Europe play for second or third division sides. But somehow we've created a solid, penetrative unit and ... I've started to dream of a place in the finals!"

One traditional minnow who are even closer to a place in the finals are Botswana, who are six points clear at the top of Group K, in which, by dint of it being the only five-team group, both the first and second place teams secure automatic qualification. Unbeaten in their past eight matches under the manager Stan Tshosane, the Zebras go to Chad knowing that a win will secure qualification for the finals.

Much of their success has been down to the fact that, unlike CAR, Botswana have benefitted from staging regular training camps and friendlies, and hiring specialist fitness coaches and scouts. They do not have a single player based in Europe (they all play either in Botswana or South Africa), which has facilitated these get-togethers. They must contend with a couple of important absentees this weekend, notably the winger Sekhana Koko, but can at least call on the services of the striker Jerome Ramalthkwane, who has scored four goals in five qualifiers despite hardly playing any club football over the past two years.

This weekend will also witness Samson Siasia's first competitive match as manager of Nigeria, defending champions Egypt heading to South Africa in the hope of correcting a faltering campaign, and a high-stakes derby between those north African CAR-pursuers Algeria and Morocco.

But perhaps the most intriguing game will be in Dakar, where Senegal could confirm that they are once again a force to be reckoned with by beating Cameroon. The generation that thrilled at the 2002 World Cup never built on that performance and nor did the country's football authorities, as the domestic league temporarily collapsed, and the FA and the national team were beset by squabbling until, following action by local clubs, some order was finally restored. Now Senegal have a new generation of players and a manager, Amara Traoré, who seems to have instilled drive and cohesion.

Senegal look particularly strong up front. Their strikers are thriving all over Europe: Moussa Sow is the top scorer in Ligue 1, Papiss Demba Cissé is the second highest-scorer in the Bundesliga, Dame Ndoye is top scorer in Denmark and Demba Ba is helping to revive West Ham. Throw Mamadou Niang, who is still banging in goals both for his country and for Turkish league leaders Fenerbahce, and it is not hard to understand why Senegal scored 11 goals in their first two qualifiers. Given that their defence includes the pillars of the two meanest rearguards in France (Marseille's Souleymane Diawara and Rennes' Kader Mangane) and that Cameroon appear to be a in a muddle under the new manager Javier Clemente, the chances of Samuel Eto'o outscoring the hosts on Saturday do not look high.