All four goals came in the second half at the Stade Prince Louis in Bujumbura to see the Zambian club advance 4-2 on aggregate after winning the first leg 2-0 last Friday in Ndola.
The host were the better side on their artificial turf with midfielder Oliver Sabumukama giving Zesco's defence a torrid time throughout with his sleek play.
And it was Sabukumana who broke the deadlock in the 49th minute when he slammed past two midfielders and defenders before slipping past goalkeeper Jacob Banda to make it 1-0.
Zesco striker Jesse Were equalised in the 61st minute in the midst of pressure from a determined Messager.
The host were back in the lead in the 86th minute through Abdoul Amini who ghosted pasted defender Jackson Kapumbu to fire in the ball on the near right post.
However, Zesco refused to die and equalised in dramatic fashion deep into the four minutes of stoppage time through defender David Owino who tapped-in the equaliser from another Kapumbu free-kick.