In 2013, Rodriguez had her breakthrough season, she won the 2013 Mediterranean Games in Mersin beating Greek gymnast Varvara Filiou (silver) and France's Kseniya Moustafaeva (bronze). In 2014 season, Rodriguez achieved her highest placement in the World Cup series at the 2014 Lisboa World Cup finishing 4th in all-around. She qualified to 3 event finals and won a bronze in clubs. On May 30-June 1, Rodriguez competed at the 2014 Minsk World Cup and finished 14th in all-around. On June 10–15, Rodriguez competed at the 2014 European Championships and finished 10th in all-around. at a press conference, Rodriguez announce her plans to continue competing until the 2016 Olympic Games in Rio de Janeiro, Brazil. On August 8–10, Rodríguez competed at the 2014 Sofia World Cup finishing 11th in all-around finals. On September 22–28, Rodriguez placed a career high at the 2014 World Championships finishing 10th in the all-around finals with a total of 68.448 points and qualified to an event final (in ribbon) for the first time at Worlds. In 2015, Rodriguez competed at the 2015 Holon Grand Prix finishing 13th in all-around. Rodriguez finished 15th in all-around at the 2015 Berlin Grand Prix. On June 15–21, Rodriguez competed at the inaugural 2015 European Games where she finished 13th in the all-around. In July, Rodriguez won the all-around gold at the Izmir International Tournament ahead of Jana Berezko-Marggrander. In August, Rodriguez finished 14th in the all-around at the 2015 Sofia World Cup. On September 9–13, Rodriguez competed at the 2015 World Championships in Stuttgart and finished 9th in the All-around finals with a total of 70.248 points.