Lethal striker Simon Msuva scored a superb goal for Yanga in the 39th minute when he coordinated well with Donald Ngoma and Justine Zulu.
The goal lasted for 38 minutes before Ghanaian striker Kwame leveled for the visiting side Zanaco in the 78th minute.
Zanaco looked weak in the first half but improved as time went on.
The results put Yanga in a difficult situation on their away return leg match set for next Saturday in Lusaka.
The Zambia champions will need a goalless draw while Yanga will need to win at least 1-0 for them to advance into the group stage.
Losers of the return leg will be dropped to the Confederation Cup.
Zanaco booked their date with the defending Mainland champions, after making it out of the preliminary round, with a 1-0 away win over APR of Rwanda on February 19, in Kigali to advance by the same scoreline.
Yanga qualified to face the Zambian side after eliminating Ngaya de Mde of Comoro with a 6-2 aggregate.
Meanwhile, the country’s envoys in the CAF Confederations Cup Azam FC face Mbabane Swallows of Swaziland in Dar es Salaam in the first leg today.
The first round, first leg match will be played at Azam Complex Chamazi and is set to kick off at 8:30pm.