Ahoure, with two previous world indoor silvers to her name, clocked an electric 6.97 seconds down the blue track in Birmingham, the fastest time run over the sprint this season.
Ahoure's teammate Marie-Josee Ta Lou (7.05sec) took silver by five-thousandeths of a second in a photofinish from Switzerland's Mujinga Kambundji.
It was not only a first world indoor gold for Ivory Coast but also the first time an African sprinter, male or female, has won the 60m title.
"I knew he was watching from up there," she said. "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. I have so much pent-up up emotion now."
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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.
"The most important thing I knew would be getting out of the blocks and executing my race, focusing on my lane.
"It's huge to get gold and silver. The Ivory Coast is on top, we're so happy and hopefully soon we'll be able to take over the whole podium!"
The local crowd were earlier given a treat when Katarina Johnson-Thompson racked up 4,750 points to win the pentathlon, her first global title.
She kept a cool head in the final event, the 800m, winning in a season's best of 2:16.63, with Austria's Ivona Dadic taking silver (4,700 points) and Cuban Yorgelis Rodriguez bronze (4,637).
"It's been a very long hard day but it's definitely been worth it. As always in the pentathlon there are highs and lows throughout the day. I am so happy to have won," said Johnson-Thompson.
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South Africa's world outdoor champion Luvo Manyonga was upstaged by Cuban teenager Juan Miguel Echevarria in a thrilling men's long jump competition that went down to the wire.
Echevarria went out early to 8.28m, Manyonga responding perfectly after botching his first two efforts to soar out to 8.33m on his third to advance to the showdown between the top eight jumpers.
The Cuban landed a personal best of 8.38 before the South African replied with 8.44.
Defending champion Marquis Dendy of the United States then went out to 8.42 with his fifth effort. But up stepped Echevarria, 19, to nail 8.46m for a memorable gold ahead of Manyonga, with Dendy rounding out the podium.
"I think I'm in the peak of my career. I'm feeling very physically strong."
The other gold on offer went the way of Hungary as Anita Marton threw 19.62m to win the shot put ahead of Jamaica's Danniel Thomas-Dodd (19.22) and China's Lijiao Gong (19.08).
France's Kevin Mayer, world outdoor champion and Olympic silver medallist in the decathlon, was in overnight pole after the first four events in the seven-discipline heptathlon, with the 60m hurdles, pole vault and 1,000m to come on Saturday.