A tense, tightly fought contest in front of a capacity 50,000 crowd in Brisbane had ended goalless after both 90 minutes and then extra time had failed to provide a breakthrough between two evenly matched sides.
Fowler twice had opportunities to fire Australia ahead either side of half time only to be denied firstly by a brilliant goal-line block from French defender Elisa de Almeida and secondly by Wendie Renard’s intervention.
That was nothing though compared to the drama of what proved to be the longest and most nerve-wracking penalty shootout in Women’s World Cup history.
The Matildas twice had penalties to win the match and reach the semi-finals only to spurn both opportunities.
But finally, at the third time of asking, Cortnee Vine successfully converted from 12 yards to clinch the most amazing 7-6 victory and send the hosts into ecstasy.
Fowler was amongst those to successfully convert for Australia in what made for compelling – and nerve-shredding – viewing for those at the ground and the millions more watching around the globe.
There was even a moment of VAR controversy during the shootout at 6-6 with France’s Kenza Dali seeing her initial spot kick saved by Australian keeper McKenzie Arnold – who saved three of France’s penalties - only for the kick to be retaken with Arnold’s foot being adjudged off the line.
Incredibly Dali saw her retaken spot kick saved again by Arnold who had earlier missed the chance to fire Australia through only to blaze wide.
Clare Hunt then followed suit by missing her spot-kick only for France’s Vicki Becho to hit the foot of the post with the scores still tied at 6-6.
That set the scene for Vine who demonstrated nerves of steel to fire home to the left of the France keeper and spark scenes of unbridled joy.
It means Australia are through to their first World Cup semi-final and they will meet the winner of the England v Colombia quarter-final which takes place later on Saturday morning.