Katongo netted twice inside the opening 10 minutes, the first coming with a deflection off defender Wissem Abdi and the second two minutes later from a shot on the edge of the penalty area.
Swiss-based striker Yassine Chikhaoui hit the post for Tunisia midway through the first half and then reduced the deficit two minutes after the break.
In another warm-up match, defending champions Egypt beat Namibia 3-0. Saturday’s match in Aswan was the first of three planned preliminary matches for the Pharaohs who are still sweating on the availability of frontline striker Ahmed ‘Mido’ Hossam who is suffering from a groin injury.
The Middlesbrough forward has a knee injury and is unsure of his fitness for the tournament, which starts on January 20.
Namibia played their first match under new Dutch coach Arie Schans, who has had less than month to work with the team. His predecessor, the Zambian Ben Bamfuchile died at the end of last month, casting a shadow over Namibia’s preparations.
All but two of the 16 Nations Cup finalists will play warm-up internationals over the next three weeks before the tournament kicks off, reports Mark Gleeson.
Cameroon had planned a match against Kenya in Nairobi but the post-election violence in the East African country have seen the Indomitable Lions switch their preparations to Burkina Faso. To date, they have no matches planned and will not have played an international since their last qualifier in September.
Guinea play no warm-up internationals but will get match practice against club opposition in Marbella, Spain, where they have will begin preparations this week. Among their planned opponents are Fiorentina and Borussia Dortmund.
Nigeria and Sudan are training in Malaga while Benin have gone to Brazil for a 10-day camp before heading to Burkina Faso for a warm-up match against Senegal on Jan. 17.
Angola have been in Portugal since before Christmas for their preparations.
Tunisia hosted Zambia at Rades yesterday (Sunday) before a flurry of fixtures next week, which sees matches in Abu Dhabi, Spain, Portugal, Morocco and South Africa.
Under Fifa rules for continental championship, clubs must release their players for preparations a fortnight before the start of the tournament, setting yesterday (Sunday) as the deadline for squad members to join up.
But there are likely to be some exceptions, notably Ghana’s Michael Essien who officials said would likely be allowed to play for Chelsea against Tottenham Hotspur on January 14.
Meanwhile midfielder Mohamed Barakat has been ruled out of Egypt’s squad. Barakat, who helped the Pharaohs win the tournament two years, has struggled with a knee injury for the past few months.
Already sidelined from the three-week tournament are Ghana captain Stephen Appiah and key Morocco midfielder Mbark Boussoufa.
The Ivory Coast striker Didier Drogba is doubtful after knee surgery last month.
Meanwhile, veteran goalkeeper Khalid Fouhami has been handed a surprise recall to Morocco’s Nations Cup squad. Fouhami has not played for the Atlas Lions for more than two years.
But he was named by coach Henri Michel in a party of 23. It was Fouhami's goalkeeping error which saw Morocco beaten 2-1 by hosts Tunisia in the 2004 Nations Cup final.
However, Morocco will be without injured midfielder Mbark Boussoufa when they go in search of what will only be their second Nations Cup title.
Spain-based Mohamed Yaacoubi and former Ajax striker Nourdin Boukhari have been dropped.
Morocco play Namibia in their Group A opener in Accra on January 21 and also share the group with Guinea and hosts Ghana.
