The Astana rider finished six seconds ahead of Italian Domenico Pozzovivo, who had gone into the time trial with a 4sec lead over the Slovenian but finished 10th on the day, 10 seconds short of his rival.
The time trial was won by another Slovenian, Kristjan Koren of Liquigas, who finished third overall.
Italy’s Adriano Malori was just one second behind Koren, with South Africa’s Orica rider Daryl Impey third on the day.
"Happy with the win (but) not happy with today's (time trial)," Brajkovic posted on his Twitter account. "Need to improve."
Brajkovic, 28, had never won his home tour before and now has three major UCI Tour wins, adding to the 2010 Criterium de Dauphine and 2007 Tour of Georgia.