Kozak and teammates Gabriella Szabo, Tamara Csipes and Krisztina Fazekas-Zur won the women's K-4 500-metre sprint in 1:31.482, ahead of silver medal-winning Germany and bronze-winning Belarus.
The victory is the latest in Hungary's history of dominance in the sport. Hungary's women won the event at the 2012 Games and took silver in the K-4 at the 2008, 2004 and 2000 Olympics.
Image credit: Eurosport
Brazil's Queiroz dos Santos secures third Olympic medal, misses out on gold
Kozak is the first woman to win three gold medals in canoe sprint in a single Olympic Games and the third athlete in the sport overall, after Vladimir Parfenovic of the Soviet Republic in 1980 and Ian Ferguson of New Zealand in 1984.
If that feat sounds unbelievable, Kozak herself has yet to process it.
I'm very happy," Kozak said after the race. "I think I need some time until I believe it.
Kozak is now one of her country's most decorated Olympians, having won five gold medals and a silver. Her two other gold medals in Rio were in the women's K-2 500m on Tuesday and K-1 500m on Thursday.
Great Britain's Liam Heath sprints to gold in the 200m kayak
GB's Heath and Schofield secure dramatic silver in 200m kayak final