Tunisia, who were group favourites, suffered a shock home defeat by Botswana at the start of qualifying last month but goals from Khaled Korbi, Issam Jemaa and Fahid Ben Khalfallah handed them a 3-1 win in Ndjamena to restore their hopes.
The Tunisians led 2-0 at half-time. Chad's second half consolation goal came from Ezekiel Ndouassel.
Botswana, who have never qualified for the finals, drew 1-1 in Malawi and now have seven points from three matches. Tunisia are second with three points from two games.
The visitors took a 62nd-minute lead through Jerome Ramathlakwane but Dave Banda equalised for Malawi 12 minutes later.
Group K is the only one of the qualifying sections with five teams. The other 10 groups get underway next month.
The finals are being co-hosted by Equatorial Guinea and Gabon.
