Two of the saves were made by substitute goalkeeper Timothy Fayulu, who replaced Lionel M’Pasi in the final minute of extra time.
DR Congo was called Zaire when the country qualified for the only time in 1974. It was not a happy debut, as they failed to score and conceded 14 goals, including nine against Yugoslavia.
Nigeria lie 19 places above DR Congo in the world rankings and were pre-match favourites, but DR Congo recovered from conceding early to look the likelier winners the longer the match proceeded.
Nigeria, who needed 78 minutes to break the scoring deadlock in a 4-1 semi-finals victory over Gabon three days ago, were ahead within three minutes against the Congolese.
A cross was only partially cleared, and a hard, low shot from outside the area by Brentford midfielder Frank Onyeka was deflected by Burnley defender Axel Tuanzebe past M’Pasi.
DR Congo slowly recovered from the shock of falling behind so early against the Super Eagles and levelled after 32 minutes.
Veteran forward Cedric Bakambu crossed, and when Nigeria captain Wilfred Ndidi failed to control the ball in the six-yard box, Mechak Elia pounced to beat goalkeeper Stanley Nwabali.
– Osimhen injured –
Star Nigeria striker Victor Osimhen, scorer of five goals in his last two international appearances, suffered an injury late in the opening half and was replaced by Akor Adams for the second period.
As the second half of regular time progressed, the teams became increasingly cautious, especially Nigeria, who almost gifted the lead to DR Congo on 83 minutes.
A defensive mix-up involving Nwabali ended with DR Congo substitute Mahmoud Mayele just failing to snatch the lead.
DR Congo thought they had taken the lead 19 minutes into extra time, but the Moroccan referee disallowed the goal, ruling scorer Noah Sadiki had committed a foul.
Victory qualifies the Congolese for a six-nation inter-confederation mini-tournament in Guadalajara and Monterrey from March 23.
The African representatives are the third nation to secure a place after Bolivia and New Caledonia, and the other three slots will be filled on Tuesday for a competition that excludes Europe.
Iraq host the United Arab Emirates in Basra after the first leg of the Asian decider finished 1-1 last Thursday in Abu Dhabi.
Jamaica and Panama are the frontrunners to be the two Central America/Caribbean flagbearers, but Suriname, Curacao, Honduras, Haiti and Costa Rica are other possible qualifiers.
The two highest-ranked teams will receive byes into single-match finals, while the other four meet in single-match semi-finals. The winners of the two finals go to the World Cup.
Hosted by the United States, Canada and Mexico, the global showpiece during June and July 2026 will feature a record 48 nations, up from 32 at the last edition in Qatar three years ago.
The nine automatic African participants are Algeria, surprise packets Cape Verde, Egypt, Ghana, Ivory Coast, 2022 World Cup semi-finalists Morocco, Senegal, South Africa and Tunisia.