D.R. Congo now await the draw on Thursday for the inter-confederation play-off in March, where six teams will chase two places at the 48-team finals.
Captain Chancel Mbemba converted the decisive kick after Congolese substitute goalkeeper Timothy Fayulu, brought on a minute before the shootout, made two saves in the shootout.
Frank Onyeka had Nigeria ahead in the third minute, but Meschack Elia equalised for the two sides to be level 1-1 after extra time.
The mini-tournament in Rabat was for the best runners-up across the nine African qualifying groups, whose fixtures were completed last month, with the nine winners automatically booking a berth at the World Cup in Canada, Mexico and the USA next year.
Nigeria, who have been to six previous World Cups, were off to a perfect start as the Congolese cleared an early cross but only onto the edge of their penalty area, where Onyeka snapped up the ball and powered home an effort, helped into the net by a slight deflection off Axel Tuanzebe.
But the Congolese could have been level within nine minutes had Ngal'ayel Mukau not put his close-in effort over the crossbar after Nigeria goalkeeper Stanley Nwabali had flapped at the ball.
They did equalise in the 32nd minute after Alex Iwobi had been stripped of possession inside the Congolese half, and a quick counter saw Cedric Bakambu square for Elia to score despite the efforts of Nigeria captain Wilfred Ndidi to intercept the ball.
A clever backheel at a corner early in the second half from Bakambu saw Nwabali make a sharp stop, and there looked a decent penalty shout for the Congolese as Noah Sadiki was upended by Benjamin Fredrick in the Nigeria box in the 55th minute, but the referee did not show any interest, and there was no VAR check.
Congo looked more ambitious as the contest wore on, but it was characterised by a wary approach from both sides, keen not to make any mistakes with so much at stake.
Nigeria needed extra time to get past Gabon in their Thursday semi-final and looked much more fatigued than their opponents, who beat Cameroon inside 90 minutes in their semi later the same night.
There were two opportunities in extra time on either end, with Nigerian substitute Tolu Arokodare heading over, and then with the last effort of the game, Mbemba had his effort saved by Nwabali.
DR Congo competed at the World Cup in 1974 when the country was still known as Zaire.