The 31-year-old from Sollefteå, Sweden, is a 12-time National Champion, and currently holds the blue and yellow cross jersey in both Road Race and Time Trial.
Darke, who won silver in the H3 hand cycle time-trial at Greenville in 2014, finished the 14-kilometre effort in 30:16.15, with the world title going to Italian Francesco Porcellato in a time of 27:53.94.
Storey took a comfortable victory, finishing over two minutes ahead of second placed Polish rider Anna Harkowska.
“We were outnumbered a wee bit as well, because me and Amy were just by ourselves.
Wiggle Honda Pro Cycling’s riders scored an incredible three wins in a single day today, as Belgian Champion Jolien D’hoore won both stages 2a and 2b in the BeNe Ladies Tour
"It was very tough today, especially with the wind," said the freshly crowned European Games champion.
The 25-year-old Belgian Champion beat compatriot Kelly Druyts (Topsport Vlaanderen Pro-Duo) to the line, at the end of the 124km race.
King's performance, against most of the top riders in the British domestic peloton, confirms that the 24-year-old has recovered from her horrific crash of last November.
The Philly Classic sees the World Cup return to the United States for the first time since its previous incarnation.
The Japanese Champion managed to bridge across to a late break from Gracie Elvin (Orica-AIS) and Ellen van Dijk (Boels-Dolmans) but was unable to compete with the two faster sprinters on the slightly uphill finish.
The Netherlands took the first world title of the evening in the women's Scratch Race, their first gold medal of these championships. Kirsten Wild won the rainbow jersey. The final title of the night went to Germany's Kristina Vogel
"This is my first World Championships," stated Wiasak, "I have never even won a national championship, so it is fantastic to get a World title.
Russia's Anastasia Voynova took gold after finishing in the bronze medal position last year, while world record holder Anna Meares of Australia retained silver, and defending champion Miriam Welte of Germany dropped to bronze. UCI ©Guy Swarbrick
The 2015 UCI Track Cycling World Championships opened in St-Quentin-en-Yveline, France, on Wednesday with a world record time set, plus a win for the host nation.
The staging of the world championships in the Lee Valley VeloPark at Queen Elizabeth Olympic Park