The visitors were trailing 1-0 from the first leg played in Lusaka three weeks ago and now bow out 3-1 on aggregate. They showed some resilience when they equalised in the 48th minute through Musonda Mwape.
Pirates were ahead in the first half but Zanaco showed some signs of improvement and could have progressed to the next round if they beat the hosts 2-1. The outcome was the opposite.
It was Pirates who finished stronger with a 2-1 win and they progress to the next round where they will face four-time African club champions TP Mazembe in the pre-group stage.
Zanaco complete a disastrous first four months of Zambian football in which the national team were eliminated from the Africa Cup of Nations in the first round while Power Dynamos were also eliminated in the early stages of the Confederations Cup.