World champion Johnson and pilot Morton claimed victory in a Paralympic record of 1:08.919.
Great Britain's Aileen McGlynn and Helen Scott came second in 1:09.469 and New Zealand's Phillipa Gray and Laura Thompson were third in 1:11.245.
McGlynn had won the title at the last two Paralympics, and the Australians were thrilled to triumph.
'I could feel them nipping at our heels and it was great motivation for us to come in and try our best, considering it's their home turf and the track is really fast,' Johnson said.
Morton added: 'I tried to let Flick know that we'd won because the crowd goes off and she can't quite see the scoreboard, but I think she knew.'
A disappointed McGlynn said: 'This was our main focus. We came into it really well prepared and we thought we had it. It's bike racing, it doesn't always go the way you want it to.'
Britain's Mark Colbourne is set to ride for gold in the men's Individual C1 Pursuit after qualifying fastest in a world record of 3:53.970.
Colbourne finished second to Li Zhang Yu in the Individual C1-2-3 1km Time Trial on Day 1 and watched the Chinese rider set a world record of 4:00.235 in Pursuit qualifying before improving the mark himself to set up a duel between the pair.
China's Liang Guihua was the fastest qualifier in the Individual C2 Pursuit, clocking a world record of 3:45.828 to set up a final meeting with Tobias Graf of Germany (3:47.799).
In the men's Individual C3 Pursuit, Joseph Berenyi of the USA set a world record of 3:36.148 in the first heat.
Great Britain's 2008 champion Darren Kenny can win bronze at best after qualifying in 3:37.977.
Team-mate Shaun McKeown was one of three riders to dip beneath Kenny's world record set in Beijing, advancing in second place in 3:36.427.
Kenny advanced in fourth and was poised to meet David Nicholas of Australia (3:36.757) in the ride-off for third place.