Lithuanians Mindaugas Griskonis and Saulius Ritter had to be happy with the silver, while the bronze went to Norway's Kljetil Borch and Olaf Tufte.
Brothers Martin and Valent Sinkovic won the silver medal at the Olympic Games in London four years ago, rowing in the Men's quadruple sculls together with Damir Sain and Damir Martin.
Since starting to compete in the double sculls in June 2014, the Sinkovic brothers have won 29 races in a row.
This is Croatia's second gold medal at the Olympic Games in Rio de Janeiro after Josip Glasnovic won the gold in the Men's trap.
The Sinkovic brothers have another five medals from world competitions (4 golds and 1 bronze) and three medals at European championships (2 golds and 1 silver).