Perry was Australia's driving force as the tourists reached 328-7 at the close of play in the lone Test of the multi-format series at Trent Bridge.
In the biggest moment of a dramatic day, Perry overturned an lbw verdict off Lauren Filer's first ball at international level.
Perry, who had scored only 10 at the time, went on to reach her fifth 50-plus score in 10 Tests against England.
Just as Australia looked set to take a stranglehold on the Test, Ecclestone dismissed Jess Jonassen and Australia captain Alyssa Healy, for a duck, in the same over.
Filer eventually claimed the prize scalp of Perry as she eyed a century, while slow left-armer Ecclestone bowled Tahlia McGrath, who smashed 61 in a 119-run stand with Perry.
The five-day Test is worth four points in the series and will be followed by three Twenty20 internationals and three one-day internationals.
After the thrilling first men's Test between England and Australia earlier this week, it was the women's turn to seize the spotlight.
Trying to regain the urn for the first time since 2015, England were cheered on by an attendance of 5,545 - the largest crowd on a single day for a women's Test in the country.
England captain Heather Knight, who promised to "entertain and inspire" on the eve of only the second five-day women's Test in history, was attacking with her field settings after the hosts were asked to bowl.
But Australia, buoyed by their T20 World Cup triumph earlier this year, were in control at 226-3 before losing three wickets for 12 runs in the space of 24 balls to give England renewed hope.
Annabel Sutherland (39 not out) and Alana King (seven not out) will hope to blast Australia towards 400 when play resumes on Friday.
