Scoring chances were few during a dreary duel that rivalled the goalless deadlock between hosts Equatorial Guinea and Burkina Faso for the worst game so far of a generally entertaining tournament.
The result left the sides sharing second place, two points behind Tunisia and one ahead of Zambia, with one series of matches to come next Monday.
Tunisia snatched a 2-1 victory over wasteful Zambia in the first match of a double-header with captain Yassine Chikhaoui nodding an 89th-minute winner.
Cape Verde shaded a first half that never scaled great heights before a capacity 5,000 crowd at Nuevo Estadio de Ebebiyin in the north-east Equatoguinean town.
Kuca was not far off target with an early angled shot and captain Babanco saw his medium-range free-kick whizz just over the crossbar.
DR Congo suffered a serious blow midway through the opening half when captain and West Bromwich Albion midfielder Youssouf Mulumbu came off with a suspected hamstring injury.
Issama Mpeko took over as skipper and Nelson Munganga came on for the Leopards, who were struggling to put Cape Verde goalkeeper Vozinha under sustained pressure.
Calu had a chance to nudge the islanders ahead just past the half-hour, but his powerful header off a free-kick flew straight to veteran Congolese shot-stopper Robert Kidiaba.
Kuca was hyper-active in attack for the Blue Sharks and found space on the left flank but, when he cut in, his shot was blocked by a defender.
DR Congo finally threatened in first-half stoppage-time and had their first shot on target which Vozinha saved comfortably from Yannick Bolasie.
It was the first glimpse of the pacey Crystal Palace winger, who starred in a 1-1 draw with Zambia four days ago.
There was less excitement in the second half and rival coches Rui Aguas and Florent Ibenge made substitutions to try and stimulate greater attacking menace.
Heldon, whose goal earned a 1-1 draw with Tunisia last Sunday but who started on the bench against the Congolese because of a toothache, replaced Kuca.
And an ineffective Bolasie was pulled off with Chechnya-based Jeremy Bokila coming on.
Kidiaba, at 38 the oldest player at the 2015 Cup of Nations, came to the rescue five minutes from time, making two saves in rapid succession after a corner was not cleared.
The dreadlocked shot-stopper was the Congolese saviour again soon after, blocking a close-range Heldon shot with his chest.