West African neighbours and former champions Ivory Coast and Ghana square off on Sunday in Bata for the title and a US$1.5 million first prize.
DR Congo have appeared twice before in third-place play-offs, losing heavily to hosts Cameroon in 1972 and pipping 1998 hosts Burkina Faso on penalties.
Equatorial Guinea are competing at the Cup of Nations for only the second time and exited at the quarter-finals stage three years ago.
There was little goalmouth action during the opening half with Crystal Palace and DR Congo winger Yannick Bolasie spurning the best chance five minutes before half-time.
He darted in from the left flank to control a through pass with his chest and leave Iban Iyanga trailing in his wake.
After allowing the ball to bounce several times, Bolasie unleashed a hard, rising shot that flew wide of the far post with goalkeeper Felipe Ovono a helpless onlooker.
DR Congo goalkeeper Robert Kidiaba -- at 39 the oldest footballer at the 2015 tournament -- had rescued the Leopards 10 minutes into the first half.
He blocked a strike from former Real Madrid winger Javier Balboa in a goalmouth scramble and, seconds later, blocked an equally close-range shot from captain and striker Emilio Nsue. The largely pedestrian half could partly be explained by the oppressive heat with the mercury touching 33 degrees Celsius for the late afternoon kick-off.
A quicker pace and more goalmouth excitement marked the second half with Kidiaba and the much younger Ovono kept busy, but as the game reached the three-quarter mark it remained goalless.
There was no lack of endeavour in the closing stages, but no goals either, with selfishness costing DR Congo a good chance three minutes into stoppage time as Lema Mabidi fired well wide with two team-mates unmarked