It was all about England's resilience as they first came back from two goals down in normal time, before producing the goods in a crazy shootout.
Sweden goalkeeper Falk had the chance to seal victory with their fifth penalty but blasted the ball over the bar.
England midfielder Grace Clinton's effort was then saved by Falk but Hampton denied Sofia Jakobsson - Sweden's second chance of securing victory.
It was fitting then, that veteran defender Bronze, playing in her seventh major tournament, should step up to the spot, knowing she had the chance to put England in the driving seat.
After she fired the ball into the roof of the net, she paused to roar at the fans behind the goal before returning to her team-mates to celebrate on the halfway line.
The 33-year-old has scored twice in the tournament and showed her experience in the crucial moment after England's defence had been ruthlessly exposed in a brutal first half by Sweden.
Jess Carter had been completely outmatched, struggling to handle Blackstenius and Johanna Rytting Kaneryd's pace down England's left-hand side, while Alex Greenwood could offer little support.
But while England's defensive frailties have been on show for a while, so has the positive impact of their substitutions and they all played a key role in the comeback.
England rode their luck, leaving it nervously late to respond and may not be so fortunate against other heavyweight opposition, but they have been here before. They know the score.