Storey, who is solely competing in road events at Paris 2024, is taking part in her ninth Games – the most ever for a British athlete.
She will look to add a 19th gold in the road race on Friday.
Among active Paralympians, Belarusian swimmer Ihar Boki has overtaken Storey in terms of most gold medals won in a career, reaching 21 after five victories in Paris.
Storey won Wednesday’s time trial in 20 minutes 22.15 seconds, putting her 4.69 seconds ahead of silver medallist Gaugain – 27 years her junior. Alana Forster of Australia won bronze.
In spite of her unhappiness at the course, Storey was delighted to extend her record as Britain’s most decorated Paralympian with her 29th medal.
She first competed in the Games at Barcelona in 1992.
Storey was particularly pleased to win gold while her two children – 11-year-old Louisa and six-year-old Charlie – watched on.
“Louisa said to me last night at dinner, ‘This is the first Games I’m going to remember’,” Storey said.
“I’m utterly delighted. I had a target to get five gold medals [in time trial]. I feel so, so proud.
“You can put the challenges aside, we race the course and prepare for it, but it is brilliant, to have friends and family here, the cheering off the start line. I’m so pleased.”
On a packed day for the British cycling team, Matthew Robertson came fifth in the men’s C2 event, while Daphne Schrager finished fifth behind Brown in the women’s C1-3.
“I enjoyed it. It was different,” Brown said of the course. “I would have liked a bit of a longer course as well, we are capable of riding a bit further, but we all did the same course on the day so make the most of it.”
Two-time Rio 2016 gold medallist Stephen Bate, who won silver on the track earlier in these Games, came fifth in the men’s B time trial, as the 47-year-old competes in what may be his final Paralympics.
Archie Atkinson, who missed out on track gold following a last-lap crash, continued the trend of fifth-place British finishes, in the men’s C4, while team-mate Blaine Hunt came 11th in the men’s C5.
