Cyclist Storey powered through her event by smashing her own world record in the heats before storming to victory in front of a frenzied crowd in the Velodrome.
Swimmer Fox, who also set a new world record in his qualifier, won Great Britain's first gold at the Aquatics Centre.
It meant the medal table had a familiar look to it as the event enters its second day – with Team GB in third, the spot where its Olympic equivalent finished.
The pair were the standout performers on a successful first day, in which British athletes also won three silvers and two bronze medals.
Storey's victory is all the more remarkable because she started her career in the pool before switching to the track.
The 34-year-old, from Manchester, now has eight Paralympic titles and 19 medals in total since making her debut in the Barcelona Games in 1992.
Speaking after her win, Storey, who was born with a partly formed left hand, said: "I always thought that if I could get off to a great start it would set up the week and hopefully that's the case.
"To get the gold medal is a dream come true."
Storey only just missed out on a place in the Olympics cycling pursuit squad, which would have resulted in her racing in both the London 2012 Olympic and Paralympic Games.
She represented the non-disabled national team at the Commonwealth Games in Delhi, coming sixth in the women's individual pursuit.
Fox, 21, who was born in Cornwall and trains in Manchester, uses a Rubik's Cube to "get into the zone" before a race.
The cerebral palsy sufferer led from the start as the capacity crowd went wild.
He said: "It was really, really amazing. When you touch the wall the crowd just roars."
Britain's first medal of the Games was won by Mark Colbourne, who completed a dramatic turnaround after fighting back from a horrific paraglider accident just three years ago.
The 42-year-old broke his back in the incident in May 2009 and needed five months of physiotherapy just to get back on his feet.
He won silver in the Velodrome, less than an hour before Storey's gold.
Colbourne, of Newport, South Wales, said: "It's very exciting. We have worked for the last 18 months towards this."
He thanked his coaches for getting him "into the best shape possible".
Colbourne's proud mother, Margaret, 70, who watched alongside his 18-year-old daughter Jessica, fought back tears of joy as she spoke of her son's achievement.
She said: "I can't tell you how I feel, I'm just so very proud of him. I only wish his dad could have been here with him. We were just ecstatic and everyone was on their feet."
Jessica said: "It's such an amazing achievement and to watch him and be here and see him achieve that is just brilliant and he's only been cycling for 18 months."
Partially-sighted Ben Quilter overcame the odds to win bronze in the under 60kg judo. The 30-year-old revealed after the event that he had torn his cruciate ligaments just seven weeks before the Games.
Swimmer Hannah Russell, 16, who has achondroplasia, a form of dwarfism, narrowly lost a duel with Oxana Savchenko as she won silver in the 400m freestyle.
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