Fellow Dane Mads Würtz Schmidt had been hailed as one of the top favorites after successfully defending his European Championship title earlier in the year.
He was in contention right to the end but finished fourth behind Britain's Connor Swift and Belgium's Florian Vermeersch, who took bronze and silver, respectively.
"I can't believe it right now. It feels unreal."
"I don't usually have a great sprint, so I just tried to find a wheel. I was quite lucky with how Connor Swift rode the finale, allowing me to stay on his wheel for the last kilometer—and then have one final burst of acceleration," said Bak Klaris, according to TV 2 Sport.
The Danish duo largely dictated the action during the final stages of the World Championship race.
However, three kilometers from the finish, Würtz Schmidt slipped on a bend and went down on the gravel. He was quickly back on his feet but had to fight to close the gap to the others.
When the sprint began with less than 500 meters to go, Bak Klaris latched onto Swift's wheel, while Wurtz Schmidt tried to pass on the outside.
In a tight finish, Bak Klaris prevailed, securing Denmark's first-ever gravel medal.
The Danes played prominent roles throughout the race, which was held near the small town of Nannup on Australia's west coast.
Andreas Stokbro and Jonas Lindberg both put in a huge effort to control the peloton and claw back time after three breakaway riders had escaped early in the day, building a lead of more than three minutes.
With 20 kilometers remaining, the last of the breakaway riders were reeled in, and Wurtz Schmidt and Bak Klaris immediately launched an attack. They were joined by Swift and the Czech rider Martin Stosek, and the quartet led the race for about ten kilometers before the Belgians Vermeersch and Stan Dewulf managed to catch them.
With roughly five kilometers remaining, the Danes broke away again on a climb—this time accompanied by Vermeersch and Swift—and this proved to be the decisive attack.