The Tunisians started the day on top of the section and were on their way to securing top spot when Ahmed Akaichi headed home in the 31st minute in Equatorial Guinea's largest city.
However, DR Congo drew level in the 66th minute when substitute Loteteka Bokila scored only moments after coming on.
With the scores tied, attention turned to events in Ebebiyin, where Cape Verde and 2012 continental champions Zambia played out a 0-0 draw.
That ensured that Tunisia went through as group winners to a quarter-final against hosts Equatorial Guinea, while DR Congo can now look forward to a last-eight tie against neighbours Congo Brazzaville after pipping Cape Verde only on goals scored.
In front of a sparse crowd at the Estadio de Bata, Georges Leekens' Tunisia side appeared determined to put the game, and their qualification for the quarter-finals, to bed as soon as possible.
The game was only 10 minutes old when Ferjani Sassi, one of three players brought into the Carthage Eagles' starting line-up following their win over Zambia, connected with an Akaichi cutback only for his shot to be cleared off the line.
A superb move down the left soon after ended with captain Yassine Chikhaoui seeing his powerful strike, that was arrowing towards the far corner, turned around the post by Congo's veteran goalkeeper Robert Kidiaba.
A goal was coming and it arrived just after the half-hour mark as Akaichi headed in his second of the tournament after Chikhaoui slipped as he tried to get his shot away.
Moments later the omnipresent Chikhaoui found the net with a thunderous volley only for the offside flag to come to the Leopards' rescue.
Tunisia, the 2004 African champions, were not prolific scorers in qualifying and they would live to regret not adding to their advantage in the second half as that man Chikhaoui blazed over from close range after good build-up play by Wahbi Khazri.
Seconds after that, DR Congo equalised to give their own qualification hopes a shot in the arm.
When the Tunisia defence failed to deal with a bouncing ball on the edge of their penalty box, Dieumerci Mbokani headed it on for Bokila, who controlled on his thigh before finishing low past Aymen Mathlouthi.
Kidiaba saved from Tunisia substitute Hamza Younes at the other end as the game finished in the draw that suited both sides.