Young Africans scored the only goal of the game in the third minute through Zimbabwean forward Thabani Kamusoko and then held on for the three points.
The Tanzanians remain bottom of Group B with four points, but are now only one behind MO Béjaïa and Ghanaian side Medeama.
Medeama host pool leaders TP Mazambe on Sunday, after which all four teams would have played five matches.
The DR Congo side have already booked their place in the next round.