Benzia, who defected from the French under-21 team and made his debut in March, scored his first goal for Algeria five minutes before the break, profiting from some sloppy home defending to turn and tap the ball high into the net.
Soudani added a second on the hour to ensure the north Africans, without injured Leicester City winger Riyad Mahrez, moved into an unassailable lead in Group J after a fourth win in five qualifiers put them on 13 points.
But it was a laboured performance on an artificial pitch in the capital of the small Indian Ocean island state in Algeria's first game since the shock April resignation of coach Christian Gourcuff whose assistant Nabil Neghiz was in charge on Thursday.
Algeria, who have won the Nations Cup once when they hosted the tournament in 1990, join neighbours Morocco as the first countries to qualify for the finals in Gabon in January.
Nations Cup qualifiers continue from Friday through to Sunday.
The last round will be held in September.