In the repechage round, Bajrang, who lost to John Michael Diakomihalis of the USA in the quarterfinals, defeated Vazgen Tevanyan of Armenia 7-6 on points to qualify for the bronze medal match.
He became the first Indian to win four medals in the championship.
Bajrang has already won three bronze medals overall. Earlier, the celebrated Indian grappler took home bronze in 2013, silver in 2018, and bronze in 2019.
India sent a 30-member team to the ongoing World Championships, but they underperformed, securing only two medals.
Ravi Kumar Dahiya, who won the silver medal at the Olympics in Tokyo, crashed out early and was unable to secure a podium finish.
Meanwhile, Vinesh Phogat also earned a bronze medal at the Championships in the women's 53kg category, joining Bajrang.
Vinesh won the bronze medal by defeating Swedish opponent Emma Malmgren 8-0.
The World Wrestling Championships was held from September 10-18 in Belgrade.