There were also home wins for Comoros and Mozambique on a busy day of 17 matches in the preliminaries for the 2027 finals to be co-hosted by Kenya, Tanzania and Uganda.
Egypt, who left Mohamed Salah at home over fears of potential injury on the artificial surface at Juba in South Sudan, ran out 5-0 winners with Omar Marmoush grabbing a double and Mostafa Zico, Ibrahim Adel and teenager Hamza Abdelkarim the other three in the Group B clash.
Brahim Diaz took advantage of sloppy defending to give Morocco the lead on the stroke of halftime away against Lesotho. The match was played in Bloemfontein, South Africa because Lesotho do not have a stadium up to international standards.
Azzedine Ounahi added a second eight minutes from time to complete the 2-0 victory that has Morocco top Group A.
Senegal had to defend tenaciously away against Ethiopia to give new coach Patrick Vieira his first win in charge after last week's draw in Mozambique. Ibrahim Mbaye scored the game's only goal after 11 minutes, having been teed up by a pass from his Aston Villa teammate Nicolas Jackson.
Mozambique went top of Group J on goal difference after demolishing Sudan 4-1 in Maputo with a double from striker Chamito, who plays his club football in the third tier of Portuguese football.
Algeria found themselves 2-0 down away in Burundi after 12 minutes but fought back to share the spoils in their Group I tie in Bujumbura.
But it was a far from convincing performance under new coach Brahim Hemdani as Mohamed Belloumi and Adil Boulbina spared Algerian blushes against a team 116 places below them in the FIFA rankings.
Comoros had a 1-0 home win in Moroni over Namibia where Benjaloud Youssef scored early in the second half.
Later on Tuesday, former African champions Ghana and Zambia play at home while Cameroon, Ivory Coast and Nigeria are away.