Dombi and Kokeny became Hungary's first winners of the event by crossing the finish line just five-hundreths of a second ahead of Fernando Pimenta and Emanuel Silva.
Martin Hollstein and Andreas Ihle of Germany took the bronze.
Dombi and Kokeny had struggled to challenge the dominant German pairing until beating them to the European title in Zagreb, Croatia in June. Buoyed by that victory, they had been the quickest qualifiers for the final by nearly four seconds.
It was Portugal's first ever medal in canoe sprint.