Fox, 21, who competes in the S7 classification, touched in one minute 9.86 seconds to knock more than half a second off his old world mark and sail through as fastest qualifier by nearly three seconds.
Fox, the 2004 silver medallist, admitted that ducking under the 1:10 barrier had been one of his long-term goals.
“I came in to the heat looking to qualify first for the final,” he said.
“I didn’t realise I’d broken the world record until I looked up at the screen and saw the 1:09.
“I’ve been wanting to go under 1:10 for a long time so I’m really happy to have done that in my first race here.”
British team-mate and world champion Nyree Kindred clocked a Paralympic record to qualify fastest for the S6 100m backstroke final.
The 2004 Paralympic champion, who missed last season to have a child with British team-mate and husband Sascha Kindred, led her race out before returning to touch in 1:27.96.
But with China’s Lu Dong also ducking under the old Paralympic record to qualify second fastest and defending champion Mirjam de Koning-Peper third fastest, Kindred insisted she is taking nothing for granted in the final.
“A few of those girls who made the final are capable of a lot more as well so we’ll just have to watch this space and see what happens,” said Kindred.
“At previous Games it’s really been about the other athletes so it’s uplifting to hear them cheering for you and it spurs you on.”
Teenager Hannah Russell will also have lane four in her first Paralympic final after qualifying fastest in the S12 400m freestyle.
The 16-year old – who holds the short course world record for the event – smashed her own British record by three-and-a-half seconds to lead qualifiers in 4:41.25.
And Russell – making her Paralympic debut – admitted she was pleased with such an encouraging performance in her first appearance of the Games.
“I’m really happy do a PB in my first race here,” said Russell. “That’s what I’ll try to do for the rest of the Games and if anything else comes along as a result, I’ll be really pleased.
“Competing in front of a home crowd in a home pool at the Paralympic Games is a dream come true for me.
“The crowd were amazing so to perform in front of them was really exciting and something I’d been looking forward to.”
Susie Rodgers also impressed on her first Paralympic appearance as she qualified third fastest for the S7 100m backstroke final.
The European champion was just 0.26 off her season’s best as she touched in 1:26.09 to progress.
“It’s good to get that first one out of the way,” said Rodgers. “It looks like it will be fast but I knew it would be.
“Backstroke isn’t really main my event but it’s great to get in and get a feel for the crowd. It’s a fantastic atmosphere out there.”