Victory would have given the Copper Bullets a significant advantage over Ghana, who visit Lesotho on Sunday, but Sudan's Malik Mohammed equalised two minutes after Jacob Mulenga found the opener on 70 minutes.
Zambia's visit to Ghana in September will therefore decide which nation reaches the third round.
Uganda have the upper hand in a tight Group J after recovering to beat Angola 2-1.
With rivals Senegal facing Liberia in Monrovia on Sunday, Uganda can enjoy a two-point buffer for at least 24 hours.
Ricardo Job gave Angola the lead in the 57th minute and five minutes later the Cranes were down to 10 men as Hassan Wasswa picked up a red card.
Uganda kept going, though, with Emmanuel Okwi's equaliser seven minutes from time preceding Fabricio Mafuta's dismissal and a winning goal from Tony Mawejje with one minute to go.
Botswana's meeting with the Central African Republic in Group A was a dead rubber but there was no shortage of entertainment in Lobatse.
The hosts twice fought back from behind to claim a 3-2 victory as the Wild Beasts struggled to hold on when Calvin Tombaye saw red in the 40th minute.
Nicaise Zimbori's 33rd-minute opener was cancelled out by the penalty that followed Tombaye's dismissal - Jerome Ramatlhakwane doing the honours.
Zimbori did restore the Republic's lead five minutes after the break only for Mogakolodi Ngele (76) and Ofentse Nato (86) to turn the game on its head.