Brignone, who took gold in the Super-G earlier in these games, was the fastest in yesterday's first run, clocking a time of 1:03.23, 0.34 seconds clear of Germany's Lena Durr.
Winner of the event four years ago, Hector was very much still in contention to retain the title, sitting joint-fourth alongside Stjernesund and Lara Colturi of Albania, on 1:03.97.
In the second run, it was another Italian who looked set to steal the headlines, as Lara Della Mea put in a superb run of 1:09.75 to move into the lead, having began the day in 14th place.
Competitors fell by the wayside, and it wasn't until Stjernesund recorded 1:10.15 that she knocked the Italian into second, taking an overall lead of 0.05 seconds.
Next up was Hector, who really attacked the course, but was down on the Norwegian at the penultimate time check, only to finish strongly and, remarkably, record an identical time as Stjernesund for the second time.
Perfect runs were needed to overhaul the Scandinavians, but neither Colturi, Durr nor Sofia Goggia could better them, meaning they still sat in gold-medal position with only Brignone to come.
With her nearest rivals from run one faltering, the Milan native could afford to finish 0.70 seconds behind the leaders and still take gold. With some of the pressure off, she put in a confident performance, finishing in 1:10.27 and taking the gold medal by 0.62 seconds.
Hector and Stjernesund share the silver, while there was disappointment for Brignone's compatriot Della Mea, who was pushed down to fourth at the last.