Kozák has competed since the late 2000s. She won a silver medal in the K-4 500 m event at the 2008 Summer Olympics in Beijing. Kozák then won a gold medal at the London Olympics in the Kayak Four (K4) 500m team event with Gabriella Szabó, Katalin Kovács and Krisztina Fazekas Zur for Hungary. She also won the gold medal in the Kayak Single (K1) 500m. She won three gold medals in the Kayak Single (K1) 500m, Kayak Pairs (K2) 500m and Kayak Four (K4) 500m at the Rio de Janeiro Olympics; a feat compounded with her reeling from a stomach infection one day before the events. The latter results made her the most successful Hungarian sprint canoer and the only female athlete to win K1, K2 and K4 at the same Olympics.