The Super Eagles were on course for a much-needed victory in the 80th minute when Esperance striker Michael Eneramo scored Nigeria's second goal only for his Tunisian club mate, Oussama Darragi, to snatch a last-minute equaliser for the north Africans.
Tunisia remain top of Group Two with eight points from four matches, two points clear of second-placed Nigeria with two rounds of matches to be played. Mozambique climbed to third place after they pipped Kenya 1-0 in Maputo.
Only the group winners will qualify for the FIFA World Cup finals.
From the kick-off, the home team took the attacking initiative with Uche and Odemwingie threatening the Tunisian goal. A combination between both strikers allowed Odemwingie to take a crack at goal, which missed the target.
Tunisia were closest to going ahead in the 20th minute when Lens striker Issam Jemaa rounded Enyeama, but his final effort hit the side netting, much to the relief of the 60,000 fans.
Russia-based Osaze Odemwingie then opened the scoring after 23 minutes when he collected a pass from the lively Ikechukwu Uche before darting past two Tunisian defenders and thundering home from inside the box into the roof of the net.
Tunisia drew level two minutes later when Sliti Nabil also produced a rocket of a shot from outside the box to beat diving goalkeeper Vincent Enyeama and, having struck back so quickly, went on to create several more chances.
Enyeama saved from Ben Saada after 36 minutes and Saada again came close to getting his name on the scoresheet when his free-kick from the edge of the box a minute later was off target.
Nigeria continued to attack on the resumption of the second half, but looked increasingly suspect when the Tunisians attacked in numbers.
Esperance striker Eneramo replaced Seyi Olofinjana for the Super Eagles and within a minute of his entrance saw his header miss the target by inches.
At the other end, Enyeama saved from the ever-dangerous Jemaa, while a minute later, Nigeria had to thank the woodwork to save them from a misdirected header by Adeleye.
Nigeria fought back and regained the lead in the 80th minute when Eneramo stabbed home after great attacking play that involved John Mikel Obi and Obinna Nsofor. However, fellow Esperance striker Darragi ensured there would be no victory party in Abuja with a last-ditch equaliser.