Yoane Wissa came closest to scoring in Korhogo in a game lacking in quality in the final third, the Brentford forward testing Aishi Manula midway through the first half and almost beating the Tanzania goalkeeper with a chip from the left-hand edge of the box late on.
A third draw in as many matches was enough for the Congolese to finish second in Group F behind Morocco, who defeated Zambia 1-0 at the same time.
DR Congo will now return to the coastal city of San-Pedro for a last-16 showdown with Egypt on Sunday.
Meanwhile, Tanzania go home after collecting just two points and finishing bottom of the group.
They have still never won a Cup of Nations match in nine attempts across three appearances at the finals.
Their campaign in Ivory Coast was disrupted by the sacking of coach Adel Amrouche following their opening 3-0 loss to Morocco.
That was after he was given an eight-game ban by the Confederation of African Football and fined for comments made about the Moroccans.
Hemed Suleiman took caretaker charge of the team in the two games that followed, but Tanzania paid dearly for failing to beat 10-man Zambia in their second match at the tournament.
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