Hunter qualified fifth, 0.40 seconds behind South Africa's Chad le Clos, while the second personal best of the day pushed Perry into sixth.
"It's always great to have another Kiwi in the marching room," Hunter said. "It's just 50m. It's one of those things where skills become so important. If one person messes up a dive, it's anyone's race. If everything goes right I've got as good a shot as seven other people to get a medal."
The disqualification of England's Ben Proud, the Commonwealth and world champion, opens the door further for the possibility of either Kiwi sneaking an unlikely medal.
"It's going to be pretty tight for those medals, especially the bronze, so a lot of those guys around 23.9 can step up and have a good swim and take it so it should be exciting," Perry, who has the heats of the 4x100m relay to take care of before the final, said.
"It's great to have the best possible result in my first event and here we are, day one, and in the finals."
As expected, New Zealand's Helena Gasson and Marris Georgia failed to progress from their 100m butterfly semifinals, while Bronagh Ryan finished last in her 50m breatstroke semi, after recording a personal best in her heat.
New Zealand's 4x100m women's freestyle team of of Laticia Transom, Marris, Doyle, Gasson finished well back in their final, upstaged by Australia who set a world record, clocking 3:30.05s to lower their previous mark of 3:30.65.