A win in Franceville, plus a draw in the other group fixture between Niger and Burkina Faso on Sunday, would have seen Congo through to the final round of play-offs as Group E winners.
However, they were unable to break down a stubborn Gabon side and will now make another attempt to progress next week when they take on Burkina Faso.
Ethiopia continue to set the pace in Group A following a 2-1 victory at Botswana.
The visitors were two goals to the good by half-time thanks to efforts from Getaneh Kebede (38) and Salahdin Ahmed (45).
Tebogo Sembowa then pulled one back for Botswana after 76 minutes, but they were unable to add to their tally.
The win keeps Ethiopia two points ahead of South Africa, who were comfortable 3-0 winners over Central African Republic.
Bernard Parker (26), Siphiwe Tshabalala (43) and Katlego Mashego (90) were the scorers for Bafana Bafana.
In Group D, Zambia consolidated their position at the top of the standings with Jacob Mulenga netting twice in a 4-0 win over Lesotho.
The Utrecht striker fired in the opener after 36 minutes, with Christopher Katongo doubling the lead in the 62nd minute.
Mulenga then made it 3-0 three minutes later before Collins Mbesuma rounded off the rout seven minutes from time.
Senegal hold a two-point advantage at the top of Group J after they claimed a draw in their qualifier with Angola while Liberia were beaten in Uganda.
The Lions of Teranga led after 23 minutes of their match in Luanda thanks to Papiss Cisse, but Afonso Guilherme ensured a share of the spoils with his 52nd-minute equaliser.
Liberia, meanwhile, succumbed to a fifth-minute strike from Tony Mawejje for their second defeat in the pool.
A last-gasp goal from Fakhreddine Ben Youssef earned Tunisia a 2-2 draw against Sierra Leone as they held on to their unbeaten record in Group B.
A victory for Nabil Maaloul's men would have carried them through to the next qualifying round, but things were not going to plan when Kei Kamara fired Sierra Leone in front six minutes before the interval.
Oussama Darragi levelled matters from the penalty spot 10 minutes into the second half but Tunisia trailed again to another Kamara strike after 72 minutes.
And the visitors' unbeaten record remained under threat until stoppage time when Ben Youssef struck.
The other group game saw Cape Verde Islands beat Equatorial Guinea 2-1, with goals from Elvis Babanco (18) and Jorge Djaniny (53).
Jonatas Obina replied for the visitors.
Ivory Coast were convincing 3-0 winners over Gambia and now lie four points clear at the top of Group C.
Despite missing the talents of striker Didier Drogba, the Elephants were always in control thanks to goals from Lacina Traore (12), Wilfried Bony (62) and Yaya Toure (90).
Tanzania remain second in the standings but lost ground on the leaders with a 2-1 loss in Morocco.
A first-half red card for Aggrey Morris proved Tanzania's undoing, with Abderrazak Hamdallah scoring from the penalty spot moments later and Youssef El Arabi then adding another early in the second half.
Amri Kiemba pulled a goal back with half an hour remaining but Morocco used their man advantage to good effect.