Meanwhile, flamboyant former Everton and Liverpool defender Abel Xavier made a losing debut as a national team coach when Mozambique fell 3-1 in Ghana.
Ben Mohamed was the toast of the Comoros, a group of islands off the south-east coast of the continent, who are ranked 26 places below Botswana in Africa.
His goal on 56 minutes ended a 20-match winless run in World Cup and Cup of Nations qualifiers since 2007, when they were thrashed 6-2 by Madagascar in their first competitive international.
Soon after the Greece-based Comorian scored, torrential rain temporarily halted the Group D game at the 5,000-seat Stade Said Mohamed Cheikh.
Nicknamed Les Coelacanthes after a pre-historic fish, Comoros share second place with Burkina Faso and Botswana on three points, three behind pacesetters Uganda.
It took just five minutes at the Accra Sports Stadium for Mozambique-born former Portugal full-back Xavier to sense that he was unlikely to make a winning debut.
A superb Abdul-Majeed Waris pass sent Frank Acheampong clear and he beat the goalkeeper at his near post to put the 2015 Cup of Nations runners-up ahead.
Four-time African champions Ghana wrapped up the points through contrasting goals from captain John Boye and Jordan Ayew within three second-half minutes.
Substitute Apson Manjate pulled one goal back by nodding a cross from captain Elias Pelembe past Razak Braimah.
Remembered for his goatee and shock of dyed blond hair when playing, clean-shaven Xavier cut an elegant figure on the touchline in a waistcoat, red and navy tie, white shirt and black slacks.
Ghana have nine points in Group H, Rwanda and Mauritius three each and Mozambique none.
South Africa-based winger Anthony Laffor scored just past the hour at Stade Du Ville in Djibouti City for Liberia, who joined Togo at the top of Group A with six points each.
Madagascar remained winless and bottom of Group B after the Central African Republic snatched a late equaliser at Stade Mahamasina in Antananarivo.
Carolus Andriamahitsinoro converted a 77th-minute penalty for the hosts and the visitors had Alexandre Youga red-carded before Moussa Limane levelled five minutes from time.
Angola and the Central African Republic share first place with four points each, 2015 Cup of Nations bronze medalists the Democratic Republic of Congo have three and Madagascar two.