Group B leaders Tunisia controlled the vast majority of the clash in Bata, but could only muster one goal through Ahmed Akaichi.
Akaichi's improvised header capped a period of utter dominance for Georges Leekens' men that saw Yassine Chikhaoui cause all sorts of trouble for the DR Congo defence.
Tunisia looked destined to pile on the misery for DR Congo and saw two goals disallowed for offside.
However, Jeremy Bokila popped up in the 66th minute to earn his side a place in the next round on goals scored with a record sixth AFCON draw in a row.
The result sees Tunisia set up a last-eight clash with hosts Equatorial Guinea in Ebebiyin, while DR Congo will face Congo in Bata.
Tunisia made three changes from their 2-1 win over Zambia last time out and should have taken the lead in the 10th minute as they looked good value for their status as group leaders in the early stages.
Akaichi picked up the ball on the right flank and drove into the area, although he arguably left it too late to square the ball to Ferjani Sassi.
The ball did eventually find its way to the midfielder around 12 yards out, but his low strike was blocked on the line by Joel Kimwaki, before Yassine Chikhaoui failed to turn Wahbi Khazri's follow-up effort in at the post.
Chikhaoui looked to be Tunisia's biggest attacking threat early on and forced a superb diving save from Robert Kidiaba after 20 minutes – cutting in on his right foot following a superb passing build-up before aiming a curling effort at the far corner.
DR Congo's first real chance came as Dieumerci Mbokani saw a curling free-kick tipped around the post by Aymen Mathlouthi, but Tunisia finally made their pressure pay in the 31st minute.
Another neat passing move saw Chikhaoui pick up the ball in the box and, after turning and squirming his way through a sea of blue shirts, he pulled the trigger, only for Akaichi to dive in with a header to deceive the goalkeeper and break the deadlock.
Chikhaoui looked to have added his own name to the scoresheet with a sublime volley two minutes later, but the linesman had already raised his flag for offside, before Ali Maaloul sent a long-range free-kick just over.
Tunisia had another goal chalked off shortly after the break when Akaichi strayed offside before sending an effort under Kidiaba, but the 2004 champions were less adventurous during the second half, choosing instead to protect their one-goal advantage.
Bokila dealt Tunisia a wake-up call when he headed narrowly over from a right-wing cross in the 63rd minute and had his side level soon after.
A long ball was headed into the path of Bokila by Dieumerci Mbokini, with the substitute sending a low effort beyond Mathlouthi.
Kidiaba tipped a Hamza Younes effort over the crossbar as Tunisia looked to regain the lead, but DR Congo held on to reach the knockout stages for the first time since 2006.
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