A goal from Lushomo Mweemba in the 38th minute proved vital in keeping Zambia’s hopes of going to the next round alive.
Zambia tops the group on six points with Cameroon relegated to second on three points alongside Mozambique who defeated Lesotho 2-1.
The 2016 Africa Cup of Nations runners thumped Mozambique 8-1 but found themselves chasing shadows against Zambia.
Zambia will face Mozambique on Tuesday in the final group match while Cameroon will be up against tail-enders Lesotho.
Only group winners will qualify to the semi-finals with one second best placed team across the three groups making the semi-finals.