It was the first defeat in 47 home matches for the Super Eagles since qualifying started 48 years ago and the first time they conceded three goals at home in an eliminator.
The Congolese Red Devils were not even supposed to be in south-eastern city Calabar having lost a preliminary tie against Rwanda.
But the Rwandans were kicked out of the competition for fielding an ineligible player and Congo got a second chance.
Celtic defender Efe Ambrose nodded Nigeria into an early lead at UJ Esuene Stadium only for Prince Oniangue to level within three minutes.
Goals either side of half-time from Thievy Bifouma — the second from a powerfully struck penalty — gave Congo a two-goal lead before Gbolahan Salami snatched a late consolation.
Defeat added to the problems haunting Nigerian football.
FIFA will ban the country if controversially-elected national football federation head Chris Giwa does not step down by early Monday.
A suspension would prevent Nigeria playing South Africa in Cape Town next Wednesday and lead to disqualification from the Cup of Nations.
Coach Stephen Keshi did not have his contract renewed after a last-16 exit from the 2014 World Cup in Brazil and guided the Eagles against Congo as a caretaker.
Ghana were another World Cup team who failed to take advantage of playing at home as Uganda forced a 1-1 draw at Baba Yaro Stadium in Kumasi.
Tony Mawejje put the Ugandan Cranes ahead on the stroke of half-time in Group E and Andre Ayew levelled from a 50th-minute spot-kick.
– Life without Eto’o –
Cameroon began life without Samuel Eto’o with a comfortable 2-0 Group D victory in the Democratic Republic of Congo.
Clinton N’Jie scored in first-half stoppage time and another France-based player, Vincent Aboubakar, added the second nine minutes from time.
The Indomitable Lions always looked likely winners against the surprisingly poor Congolese Lions at a subdued Stade Mazembe in southern mining city Lubumbashi.
Long-time Cameroon captain, striker and talisman Eto’o, 33, retired from international football last month after bagging 56 goals in an 18-year international career.
Midfielder Alex Song was also absent as he is serving a three-match ban for a red card during a disastrous Cameroon World Cup campaign in Brazil.
They lost all three group games and an incident in which Benoit Assou-Ekotto headbutted team-mate Benjamin Moukandjo during the 4-0 defeat to Croatia shamed African football.
Ivory Coast, whose participation had been in doubt as the government initially refused to allow the team from Ebola-hit Sierra Leone to play in Abidjan, won 2-1 after trailing at half-time.
Captain Kei Kamara put the visitors ahead in the other Group D match only for mid-second-half goals from Seydou Doumbia and Gervinho to swing the game in favour of the hosts.
Algeria fielded eight of the team beaten after extra time by eventual champions Germany in the second round of the World Cup when winning 2-1 in Ethiopia.
El Arabi Soudani scored on 35 minutes with a deflected shot and Yacine Brahimi doubled the lead six minutes from time at the national stadium in Addis Ababa.
Ethiopia, who spent three weeks in Brazil preparing for the Group B clash, got a stoppage-time consolation goal through a Said Saladin penalty.
Shock 2012 African champions Zambia started disappointingly in Group F as they were held 0-0 by Mozambique at Levy Mwanawasa Stadium in Ndola.