Cedric Mongongu coolly slotted home the winning penalty after Javier Balboa and Raul Fabiani missed earlier spot-kicks for Equatorial Guinea.
Both sides had opportunities to win the match in normal time with Crystal Palace's Yannick Bolasie going closest for DR Congo and Rodriguez Ruben Belima squandering a second-half chance for the hosts.
A bronze medal was a deserved reward for DR Congo after a memorable tournament in which they unexpectedly reached the semi-final.
It means hosts Equatorial Guinea finish the tournament empty-handed but can hold their head high having been ranked 118 in the FIFA rankings prior to the tournament.
4' - CHANCE! A routine cross from Equatorial Guinea is misjudged by Kidiaba in DR Congo's goal who completely misses the ball but Mongongu just about clears up the mess.
20' - CHANCE! Bolasie picks out Bokila with a delightful through-ball and the latter tries to square the ball across goal instead of going for a shot but his attempted pass is blocked and it goes out for a corner.
39' - CHANCE! Bolasie latches onto a wonderful pass from the full-back, shows his marker a clean pair of heels and finds himself behind the defence, but somehow fires the ball wide of the target! Best chance of the game so far.
52' - CHANCE! What a sitter! Mabwati produces a dazzling run, riding three or four tackles and as he bears down on goal he cuts it back to Makiadi who can't get a connection on the ball. Any sort of touch would have produced the opening goal.
57' - CHANCE! Juvenal collects the ball just outside the area, and with just one thing on his mind, he shoots at goal and sees his effort fizz just wide of the post.
65' - SAVE! Bolasie collects the ball on the flank, cuts in and produces a really dangerous shot at goal which Ovono does well to push past the post.
78' - CHANCE! Equatorial Guinea found themselves in a two vs two situation as Belima advances with the ball but instead of playing it across goal for his team-mate Nsue, he blasts the ball well over the bar. What a wasted opportunity.
- BALBOA MISSES! Over the bar! He has been poor throughout this match and that just sums up his day.
- FABIANI MISSES! Equatorial Guinea have missed their second penalty as the spot-kick is saved!
- MONGONGU SCORES! DR Congo have finished as the third-placed team in the AFCON!
A memorable tournament for both sides - Equatorial Guinea failed to impress off the pitch but on it they were a breath of fresh air. Ranked 118th in the FIFA Ranking and appearing in only their second major tournament, they caused shock after shock to reach the latter stages. DR Congo entertained throughout - a 4-2 victory over neighbours Congo the highlight - and have a medal to show for their efforts.
MAN OF THE MATCH
Cedric Mabwait (DR Congo) - Was a constant thorn in the side for Equatorial Guinea, producing two magnificent individual runs which almost culminated in goals. Scored the opening penalty of the shoot-out to settle the nerves of his team-mates.
DR Congo: Kidiaba 7, Issama 6, Mongongu 7, Zakuani 7, Kasusula 6, Makiadi 7, Mbemba 7, Mabwati 8, Bokila 6, Bolasie 8, Kage 7. Subs: Mbokani, Kabananga, Mabidi.
Equatorial Guinea: Ovono 7, Evuy 7, Rui 6, Bohale 6, Zarandona 6, Juvenal 7, Balboa 5, Randy 6, Belima 6, Kike 6, Nsue 7. Subs: Fabiani 6, Doualli 6, Maye 6.