Nyirenda’s charges are one and a half step into the next round of the qualifying series.
Lusaka Dynamos star Clatous Chama scored a brace while Brian Mwila and defender Fackson Kapumbu completed the rout in Mbabane.
It was Zambia’s biggest competitive win away in Swaziland. The last time Zambia beat Swaziland in a competitive continental fixture with significant 5-0 scoreline was 1990 in an Africa Cup qualifying fixture.
Zambia has previously posted wide scorelines (9-1) and 11-2 in 1978 both in international friendlies played in 1978.