Riyad Mahrez scored twice and 20-year-old Ibrahim Maza scored his first international goal for Algeria, one of the tournament favourites, in the 3-0 win over 10-man Sudan to move top of Group E on Wednesday.
Zidane, who was at the Moulay El Hassan Stadium in Rabat to see his son Luca Zidane keep goal for Algeria, was feted by the crowd every time he was shown on the big screens.
Luca Zidane opted to represent his grandfather's country after getting the Fennec Foxes' invitation and was given the chance to shine because of an injury to Alexandre Oukidja.
Algeria wasted little time with Mahrez sweeping in the opener in the second minute after unselfish play from Hicham Boudaoui to set him up.
Zidane was called into action shortly afterward to deny Yaser Awad on a break.
Sudan had to play all of their qualification games away from home because of the near 1,000-day old civil war ravaging the country.
Though the Algerians looked confident and played with intensity, the big chances fell at the other end, with Zidane saving again from Awad before Abdel Raouf fired over.
Salah Adil was sent off just as the rain began to fall shortly before the break with his second yellow card for a foul on Rayan Aït-Nouri, who would have been through otherwise.
But Mohammed Amoura then produced a brilliant cross with the outside of his boot for Mahrez to score in the 61st, and Baghdad Bounedjah headed the ball into Maza's path for the substitute to complete the scoring in the 85th.
In Fez, Amad Diallo's second-half strike was enough for defending champions Ivory Coast to beat Mozambique 1-0 in a rain-soaked game.
The Elephants' captain, Franck Kessie, headed the ball back and Manchester United star Diallo struck it inside the far corner shortly after the break.
Ivory Coast, who won the title in scarcely believable fashion on home ground in the last edition, missed a host of chances to finish the game with Vakoun Bayo having two good chances blocked late on.
In Group F, five-time champions Cameroon put aside recent woes to open with a 1-0 victory over neighbours Gabon as Karl Etta Eyong's early goal secured a much-needed win.
The Spanish-based striker squeezed his shot under Gabon goalkeeper Loyce Mbaba in the sixth minute after being set up by Bryan Mbeumo, the goal confirmed after a VAR check.
Cameroon, five-times Cup of Nations winners, have been to more World Cups than any other African country but have struggled lately to maintain their prominent role in the continent.
They fired coach Marc Brys three weeks ago and left goalkeeper Andre Onana out of the squad for the tournament, having missed out on World Cup qualification last month.
But they will be pleased with a winning start in a fast-tempo game in which they did enjoy better of the chances.
There was late drama in Casablanca when Edmond Tapsoba completed a remarkable turnaround as Burkina Faso scored two goals in stoppage time to beat 10-man Equatorial Guinea 2-1 in Group E.
Marvin Anieboh stunned the Stallions when he launched himself at Carlos Akapo's cross to score with a looping header in the 85th minute.
Georgi Minoungou equalised in the fifth minute of stoppage time before Tapsoba headed the winner three minutes after that.
20°C