The Congolese outfit led 2-1 from the first leg in Kinshasa but looked in danger of going out on the away goals rule when the Tunisians went ahead in the 26th minute at the Stade Taieb Mhiri in Sfax through centre-back Zied Derbali.
That effort levelled the tie at 2-2 on aggregate but the visitors, who won the tournament in 1973 and last reached the final in 1981, hit back just before the interval.
Midfielder Nelson Munganga levelled matters in first-half stoppage time to give Jean-Florent Ikwanga Ibenge's men a crucial away goal.
And Vita continued in the ascendancy in the second half, securing a place in the showpiece thanks to Ugandan striker Yunus Sentamu's 55th-minute strike, for a 4-2 aggregate success.
From there, 2006 runners-up Sfaxien could not find a way back as Vita comfortably preserved their three-goal aggregate advantage to set up a final with either ES Setif or domestic rivals and four-time winners TP Mazembe, who meet on Sunday.
Setif hold a 2-1 advantage after the first leg.
