The sides could not be separated in a goalless first leg a fortnight ago, and the second proved to be a similarly tight affair.
Mahamutsa broke the deadlock for the visitors in the 52nd minute with a superb header into the top right-hand corner of the net, leaving last year's beaten finalists needing two goals to qualify.
Substitute Iheb Msakni gave the home fans hope three minutes later when he latched on to a Youcef Belaili pass from the right to prod home from close range.
A tense closing 35 minutes ensued, but it was the Pirates who continued to press and look more likely to score again, with Lennox Bacela going close after reacting quickest to a Happy Jele header that rebounded off the post.
Tension mounted as time ticked away - a scuffle erupting after an incident involving Daine Klate and Chamseddine Dhaouadi - but the Pirates managed to cling onto their advantage and reach their first continental final since 1995.
Egypt's Al Ahly and Coton Sport of Cameroon meet on Sunday to determine who will meet the Pirates in the final.
