Chipolopolo’s Group B rivals in the 2022 FIFA World Cup qualifiers Tunisia stayed top of the pool after an away goalless draw against bottom side Mauritania.
Like Zambia, the Mauritanians are out of the race to Qatar.
The battle for a place in the final qualification round will now be between the Carthage Eagles and Equatorial Guinea.
Equatorial Guinea played to a 1-1 draw with Zambia earlier on Sunday in Lusaka to move to seven points.
Tunisia have ten points in four matches.
Two rounds of matches are remaining at this stage of the campaign prior to the final round.