The 25-year-old, fifth after the Super-G behind surprise package James "Jack" Crawford of Canada, was chasing the mark set by defending champion Alexis Pinturault three racers prior.
Schwarz, a slalom specialist, was 0.32 seconds behind Frenchman Pinturault after the first run but skied an attacking slalom, making tight, clean turns whereas Pinturault had made an error on a left-foot turn around midway down the course.
That would prove to be the difference, with the Austrian crossing the line in a combined time of 2:06.98, just four one-hundredths ahead of Pinturault's mark.
Switzerland's Loïc Meillard, taking part in his first race of these Championships, went very wide on the slalom course at a similar point to where Pinturault made his mistake but recovered well enough to win bronze, 1.12 seconds behind Schwarz.
Crawford, who began the Super-G with bib number 32 before putting in the ski of his life to pip Pinturault by 0.08 seconds, held on to a very impressive fourth place as the tricky ice conditions caught out other favourites like double speed champion Vincent Kriechmayr and Matthias Mayer, who both missed gates and failed to finish.
German Simon Jocher, who also started with a high bib number in the Super-G, placed fifth.
Speaking to FIS TV after the race, Schwarz said he enjoyed both legs of the competition.
"Both of the runs," he responded when asked which was his favourite of the two. "Super-G was pretty fun, I did a great job with three-tenths behind.
"Slalom was a little bit tricky, it was very icy, but it was fun too. So all in all, it was a good day for me."
It sets the Austrian up well for next week's technical events – parallel slalom, the team event, giant slalom and slalom remain on the calendar in Cortina.
"I'm really happy to go home with a gold medal now," he said.
"It's also a great start for me, I have a few more races, so I'm looking forward."