Both sides drew their opening Africa Cup Nations matches, meaning a win for either side would propel them within touching distance of a quarter-final spot.
But Rui Aguas' team failed to make the most of their first-half opportunities while DR Congo improved after the break, but could not find a goal.
It was the third draw in four Group B matches, following Tunisia's dramatic defeat of Zambia earlier in the day, and leaves the pool finely poised ahead of Monday's final round of matches.
Florent Ibenge's men were highly fancied heading into the competition, but must hope for an improved display against Tunisia if they are to advance.
Julio Tavares came off the bench in Cape Verde's draw against Tunisia but did enough during that performance to earn a starting berth.
It was easy to see why as he was full of imagination and found Kuca in the box following some slick passing after five minutes, only for the winger to fire high and wide.
That was a sign of things to come. Cape Verde's bright start continued as Kuca won a free-kick in a dangerous position. Babanco sent the resulting effort narrowly wide, with Muteba Kidiaba scrambling desperately across his line.
Just as that early momentum appeared to have been snuffed out, Cape Verde created their best chance of the half in the 31st minute.
It came from another Babanco set-piece, as this time the skipper curled in a wonderful cross from the left that evaded everyone except Calu at the back post, but he could only direct his header straight at Kidiaba.
That brought Aguas' side back to life and five minutes later Kuca raced through as his maker switched off, only to be denied by a well-timed block.
But the longer Cape Verde went without scoring, the more their opponents grew in confidence. Yannick Bolasie showed a glimmer of what he is capable of in the final minute of the half, driving at the defence before firing in a powerful low shot, as DR Congo finished the half on the front foot.
Ibenge's side emerged a refreshed force after the break, Cedrick Mabwati underlining that fact in the 53rd minute as he danced inside from the left and ruffled the side netting with a powerful shot.
That start to the second half promised much but, as both sides tired, the pace dropped and neither side appeared willing to risk losing the match in order to win it.
However, Cape Verde almost snatched all three points five minutes from time as they committed men forward for a corner, with Kidiaba palming Fernando Vaerla's header away before rising quickly to smother Gege's follow-up.
He was called into action once more two minutes later to deny Heldon, but, despite that late flourish, the points were shared.
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