This is the second time the Kinshasa club has reached this level of the Champions League since winning the African Cup of Champions Clubs in 1973.
CS Sfaxien opened the scoring by Zied Derbali in the 24th minute.
Vita Club equalized through Dayo Issoufou in stoppage time of the first half.
Ugandan Yunus Sentamu scored the winning goal for Vita in the 67th minute.
Vita qualify by winning 4-2 on aggregate after beaing Sfaxien 2-1 in Kinshasa this past Sunday at the Tata Raphael Stadium.
They will now wait to see who wins the second leg of the other semifinals between TP Mazembe and ES Setif on Sunday in Lubumbashi.