Unchallenged defender Rooi Mahamutsa scored with a powerful swivelling header from a corner in the 54th minute at the Rades Stadium after the first leg ended 0-0 in Soweto two weeks ago.
Esperance equalised within two minutes through Iheb Msakni but could not get the all-important second goal to reach the final for a fourth successive year.
Indeed it was the visitors who proved wasteful with a hatful of chances in a fast flowing second half, including a header against the post from fullback Happy Jele and several breakaways when they had only the goalkeeper to beat but missed.
In the final the Pirates will meet either holders Al Ahli of Egypt or Coton Sport of Cameroon who play the second leg of their semi-final in the Red Sea resort of El Gouna on Sunday. The first leg in Garoua ended 1-1.
The final will be played over two legs next month.
Pirates won the competition in 1995 in the only success for a South African club in Africa's top club competition.