In the 2013–14 season, Brânză took part in the World Combat Games in Saint-Petersburg, but failed to earn a medal after defeats against Emese Szász and Xu Anqi. She finished fifth in the first World Cup event of the season in Doha after Julianna Révész defeated her 7–8 in quarter-finals, but won the gold medal in the team event, scoring the decisive hit in additional time in the last three matches. She went on to win the Budapest Grand Prix, prevailing 15–7 against Irina Embrich in the final. She later earned a bronze medal in Saint-Maur after being stopped in semifinals by China's Xu Anqi, who eventually won the competition. After three podiums in Barcelona in 2011, 2012, and 2013, she exited the competition in the table of 8 after a 15–11 defeat against Qin Xue of China. In the team event, she led her team to the semi-finals, where Romania were defeated 35–20 by Russia. Romania then met the United States; Brânză scored the winning hit in additional time to earn bronze. The rest of the season brought her no podium placings and she lost in May her world No.1 ranking to Emese Szász.