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.
Burkina Faso ensured their bid to reach the third round will continue into the autumn by beating Group E leaders Congo 1-0 in Pointe-Noire.
A home victory would have seen the Red Devils become the first nation to book their place in the last 10 but Aristide Bance had other ideas, narrowing the gap to a single point with his 38th-minute goal at the Stade Municipale.
Gabon can still dare to dream of a first-ever appearance at the World Cup finals after inflicting a 4-1 defeat on nine-man Niger.
The Panthers struggled after cancelling out Ali Yacouba's 14th-minute opener, needing a Pierre-Emerick Aubameyang penalty to level in the 43rd minute, but Niger's indiscipline caused a late collapse in Franceville.
Kossi Dan Kowa and Kourouma Fatoukouma were both shown red cards in the final 10 minutes with Aubameyang converting from the spot after Fatoukouma's indiscretion.
Bruno Ecuele Manga found space to score seven minutes into time added on and there was even time for Aubameyang to complete a rare hat-trick of penalties.
The odds are, however, stacked against Gabon ahead of the last round of games. Paulo Duarte's men must win in Burkina Faso in September while remedying a four-goal disadvantage on Congo, who would need to lose in Niger.
Morocco claimed their first win of Group C after a comfortable 2-0 victory over rock-bottom Gambia, who remain on one point from their opening four matches.
Abdelaziz Barrada gave Rachid Taoussi's men a third-minute lead, while Montpellier midfielder Younes Belhanda doubled their advantage six minutes after half-time.
Finally, Cape Verde Islands leapfrogged Sierra Leone and into second in Group B after Nhuck's 12th-minute goal ensured a 1-0 win.
However, Cape Verde remain four points adrift of group leaders Tunisia, who also have a game in hand.