Switzerland's Mujinga Kambundji claimed the bronze.
It was not only a first world indoor gold for Cote d’Ivoire but also the first time an African sprinter, male or female, has won the 60m title.
Ahouré said: "I knew he was watching from up there. I was talking to him before the race, saying: 'Please Dad help me in the race.' I couldn't get a gold medal when he was alive."
The 30-year-old added: "It was difficult when he was sick. I battled depression and I couldn’t get out of bed. I know last year at the world outdoor championships in London I wasn’t there mentally but I’ve been able to go through the grieving process and I’m in a much better place. I can talk about my dad without bursting into tears.
“I was talking to him all day, saying: 'Papa I’m on the line here, I just need you to carry me through.'”
Jamaica's double Olympic sprint champion Elaine Thompson was fourth and Dafne Schippers of the Netherlands, the two-time world outdoor 200m champion, fifth in a field that had no representatives from the United States for the first time in indoor history.
"It's huge for Cote d'Ivoire to get gold and silver,” Ahouré added. “I know they're going crazy back home. Cote d’Ivoire is on top. We're so happy and hopefully soon we'll be able to take over the whole podium!"