Accomplished Zambian coach George Lwandamina named a strong starting line-up which consisted of internationals such as Kondwani Mtonga, Jesse Were and Lazarus Kambole.
Amakhosi eased into the play-off round after defeating Zanzibar's Zimamoto in the preliminary round, before eliminating Elgeco Plus of Madagascar in the first-round.
The hosts started the match brightly with Kenyan striker Were and Zambian forward Kambole causing havoc for the Amakhosi defence with their movement in the final third.
Zesco deservedly took the lead six minutes before the half-hour mark and it was Kambole, who hit the back of the net after the visitors' defence was exposed.
Kambole, who is known to be on the radar of Chiefs' Soweto rivals, Orlando Pirates, beat goalkeeper Virgil Vries to make it 1-0 to Zesco with Rahim Ousumanu grabbing an assist.
The momentum was with Zega Mambo and they were awarded a penalty after Were was fouled inside the by Chiefs' Zimbabwean central defender Teenage Hadebe.
The 29-year-old marksman dusted himself down to power an effort past Namibia international Vries to make it 2-0 to Zesco on the half-hour mark.
However, Amakhosi, who won the 2001 Caf African Cup Winners' Cup, took control of the match towards the half-time break and they hit the post through their star attacker Khama Billiat.
The visitors then pulled one back on through Zimbabwe international Billiat, who beat Zesco goalkeeper Jacob Banda to make it 2-1 heading into the half-time break.
Were and Kambole continued to torment the Chiefs defence after the half-time break and they managed combined to extend the hosts' lead seven minutes after the restart.
This time it was Were, who grabbed his brace to make it 3-1 to Zesco after some great work by his strike-partner and 2018 Zambian Football of the Year nominee Kambole.
Chiefs came into this encounter having scored 15% of their goals in this season's Confederation Cup between the 60th minute and 75th minute.
Billiat was a constant thorn in the Zega Mambo defence and he hit the back of the net six minutes after the hour-mark, but the goal was disallowed for offside.
Middendorp introduced Ryan Moon in the closing stages of the game as Chiefs looked to grab at least two late goals to ensure that encounter ended in a draw.
Chiefs launched late attacks, but the 2017 Confederation Cup quarter-finalists Zesco stood firm at the back and ultimately, they ran out 3-1 winners in Ndola, Zambia.
The second-leg encounter will be played in South Africa next weekend (17-19 January).