Coached by Sami Trabelsi, Tunisia struck early to take control of the contest. After 10 minutes, midfielder Ellyes Skhiri, who plays his club football for Eintracht Frankfurt, rose to head home a corner delivered by Hannibal Mejbri.
The Eagles of Carthage continued to dictate play and doubled their advantage five minutes before half-time when Elias Achouri side-footed a volley into the net from close range after a precise cross from Ali Abdi.
Tunisia might have extended their lead further before the interval, but Afcon debutant Elias Saad missed a clear opportunity to make it 3-0.
Uganda goalkeeper Salim Magoola, despite conceding three times, produced several important saves to keep the scoreline respectable, while Tunisia captain Dylan Bronn also saw a header denied.
Uganda attempted to respond by making attacking changes at half-time, introducing Denis Omedi and Travis Mutyaba. However, their efforts yielded little threat, with the Cranes failing to register a shot on target until added time.
Tunisia added a third goal 26 minutes from time when Magoola spilled Abdi's shot, allowing Achouri, who plays for Copenhagen, to pounce for his second of the match.
Omedi eventually scored a late consolation for Uganda, his effort taking a deflection on the way in. The result sent Tunisia top of Group C on goal difference, following Nigeria's earlier 2-1 win over Tanzania in Fes.
It also extended Uganda's poor record against Tunisia, who have now won all seven Afcon meetings between the sides by an aggregate score of 19-2.
Despite a debut for 17-year-old James Bogere, the youngest player in this year's group stage so far, Uganda were largely outclassed, while Tunisia banished memories of a winless 2023 tournament with an assured performance.
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