The 25-year-old from Leeds, who claimed T38 100m bronze on the athletics track on Friday night, emulated Isabel Barr’s success from 1988 in Seoul.
World champion Cox won gold in the velodrome in a world record of 35.716 seconds.
The event was factored in her favour, so her time was rounded down to 34.598secs, but she was quicker than everyone else regardless.
Moments prior to Cox’s win, there was further reason for Yorkshire celebrations when wheelchair racer Hannah Cockcroft won her third Paralympic gold medal and first of the Rio Games at the Olympic Stadium.
Cockroft, from Halifax, retained her 100m T34 title in a Paralympic record time of 17.42 seconds.
Kare Adenegan, who is 15 and from Coventry, took silver behind her team-mate.
Cox’s win comes little more than two years since she was diagnosed with multiple sclerosis in May 2014.
Dame Sarah Storey was the defending champion but fully expected Cox - with the factor in her favour - to beat her.
Crystal Lane was the 10th of 14 riders to go and clocked 37.346secs to place provisionally first, only for next rider Storey to go quicker in 37.068.
Storey, who on Thursday won her 12th Paralympic title, missed out on a medal as China’s Zhou Jufang and Ruan Jianping went quicker before Cox’s storming success.
Cox is scheduled to return to the athletics track in the T36-38 4x100m relay and T38 400m, while she is also entered in cycling’s road race on the penultimate day of the Games.
Cox is competing in two of the sports which make up a triathlon, but has admitted she cannot swim.
Elsewhere, Andy Lewis claimed Britain’s 13th gold medal and first of day three with victory in the PT2 category as triathlon made its Paralympic debut at Copacabana beach.
Triathlon made its Games debut, with world champion Lewis, a lower-leg amputee, taking gold.
“I thought that I was dreaming. I couldn’t realise that it was real,” said the 33-year-old from Lydney in Gloucestershire.
“When I came across that finish line, I held the tape in the air and wondered whether it was all real.”
Lewis had his right leg amputated through the knee after being involved in a motorbike accident when aged 16. At the time he was applying to be part of the Army Parachute Regiment and was a cross country runner for Gloucestershire.
It is little more than two years since he completed his first triathlon, but he claimed an impressive win in one hour 11 minutes 49 seconds, winning by 41 seconds from his nearest rival after moving up from fourth place at the end of the bike leg and ahead of the five-kilometre run.
Ryan Taylor was sixth - 2:31 behind - while George Peasgood was seventh in the PT4 event and Joe Townsend sixth in the PT1 event.
Townsend is a Royal Marine who lost both of his legs while stepping on an improvised explosive device in Afghanistan in February 2008.
Sabrina Fortune earlier claimed bronze in the F20 shot put at the Olympic stadium.
The 19-year-old from Chester threw a personal best of 12.94 metres as Ewa Durska of Poland won with a world record of 13.94m.
Megan Giglia, Paralympic champion in the 3km individual pursuit on day one, missed out on a medal in the 500m time-trial in the day’s first final at the velodrome.
The 31-year-old from Stratford-upon-Avon was competing in the mixed C1-2-3 category and is a C3 rider, with a lesser degree of impairment than her rivals. The event was factored in favour of C1, then C2 riders.
Giglia clocked a C3 world record of 41.252 but Holland’s Alyda Norbruis took gold with a C2 world record of 39.631, factored to 36.908.