The Carthage Eagles went two points clear with one mini-league round left after a smash-and-grab 2-1 victory over wasteful Zambia at Nuevo Estadio de Ebebiyin.
Captain Yassine Chikhaoui nodded the 89th-minute winner off a Youssef Msakni cross after Emmanuel Mayuka put Zambia ahead in the second half and Ahmed Akaichi levelled.
Akaichi, a late injury-induced inclusion in the squad, became the first player at the tournament to score two goals.
Victory was a welcome relief for the North Africans, who have eaten dinner by candlelight and slept four to a room after part of their hotel was flooded.
If the first match of the double-header was worth the entrance fee, spectators were let down by a dreary 0-0 draw later between Cape Verde and the Democratic Republic of Congo.
A game without a clearcut chance rivalled the goalless stalemate between Equatorial Guinea and Burkina Faso 24 hours earlier for the dullest to date in a largely exciting tournament.
Victory for Tunisia took the 2004 champions to the top of the table with four points while Cape Verde and DR Congo have two each and identical goal differences.
And although shock 2012 champions Zambia lie last with a solitary point, they are still very much in contention for a top-two finish and a quarter-finals place.
The Chipolopolo (Copper Bullets) remain in Ebebiyin to face Cape Verde Monday while Tunisia and DR Congo clash in Bata at the same time.
Mayuka atoned for squandering two late first-half chances by slamming a half-volley past goalkeeper Aymen Mathlouthi on 59 minutes.
But just as Senegal and title favourites Algeria did three days ago, Tunisia clawed back to snatch maximum points.
A corner was nodded across the goalmouth and unmarked Akaichi stabbed the ball in at the far post.
Zambia, who would not have been flattered by a two-goal half-time advantage, were caught napping at the death as Chikhaoui nodded past goalkeeper Kennedy Mweene.
Despite winning, Tunisia coach George Leekens continues to down play his side after insisting ahead of the game that they were not group favourites.
“We have four points, but everyone is still in contention,” said the stern-faced 65-year-old.
“In the end we deserved to win. We are not the best team — we don’t have Ronaldo or Messi — but we have a team with enormous character and great mental strength.”
Leekens added that he was happy with an Ebebiyin pitch laid just weeks ago with grass flown from Spain.
Equatorial Guinea were last-minute replacements as hosts for Morocco, who wanted the tournament postponed over fears that visiting supporters could bring the deadly Ebola virus into the country.
Outstanding Zambia winger and captain Rainford Kalaba, who tormented the Tunisians during the first half, slammed his team after a third Cup of Nations loss to the Eagles.
“I don’t know what happened to my team-mates after our goal,” he confessed. “I didn’t recognise my team.”
Coach Honour Janza was equally unhappy as Zambia stretched to six the Cup of Nations games they have played over four years without a win.
“The players have their egos and it is up to them to play as a team and not as a collection of individuals,” he said.
Cape Verde came close to snatching a late winner over DR Congo in a dour match that had goalless draw written all over it long before the final whistle.
But veteran goalkeeper Robert Kidiaba came to the rescue with two reflex saves from a corner followed by the brave block of a Heldon shot.
DR Congo lost captain Youssef Mulumbu midway through the first half with a groin injury and must undergo tests.