The 23-year-old Ivorian scored the only goal, but missed a late sitter in a match moved to Zanzibar off the Tanzanian coast because the pitch in Dar es Salaam was unplayable.
Ahoua scored direct from a free-kick close to the touchline in first half added time before a capacity 15,000 crowd at Amaan Stadium.
His shot eluded everyone in a crowded goalmouth, including Stellenbosch goalkeeper Oscar Masuluke, who started in place of injured captain Sage Stephens.
There was a hint that Simba star Kibu Denis might have been offside and it took several minutes before the Congolese referee signalled a goal.
It was a deserved lead as Simba dominated possession and attacked down both flanks with pace while Stellenbosch threatened to score only once.
Stellenbosch, competing in the African equivalent of the UEFA Europa League for the first time, improved in the second half without seriously troubling Simba goalkeeper Moussa Camara.
Deep in added time, Ahoua squandered a great chance to double the lead when he sped past Masuluke. He then poked the ball wide of the post when a goal seemed inevitable.
"We cannot be happy with a 1-0 scoreline at home, especially when we had opportunities to win by two, three, even four goals," said Fadlu Davids, the South African coach of Simba.
"It was vital that we kept a clean sheet, but I am expecting a much better performance in the return match."
In the other first leg, Youssef Mehri scored after just 13 seconds to set up title favourites Renaissance Berkane of Morocco for a 4-0 home victory over CS Constantine of Algeria.
Mehri scored with a low shot from close range. A powerful header from Senegalese Paul Bassene doubled the lead before half-time.
An Oussama Lamlaoui brace in the second half completed the rout. Berkane have won 10 of 11 matches in Africa this season, drawn the other, scored 25 goals and conceded one.
