The duo, representing the Russian Federation, finished in front of Yelyzaveta Hubareva and Ilia Kovtun from Ukraine.
That's the first success for Russian gymnasts at the event since 2014, when Daria Spiridinova and Nikita Ignatyev triumphed.
Italy completed the podium with Alice D'Amato (who replaced the injured Giorgia Villa) and Stefano Patron edging out home favourites Lena Bickel and Noe Seifert of Switzerland in the small final (28,400 vs. 25,450).
Melnikova's 2021 keeps getting better and better.
Just three days after claiming an impressive win at the Arthur Gander Memorial in Morges, the Russian Federation athlete provided another convincing performance in Zurich.
In the final against Ukraine both couples made mistakes: Hubareva fell twice from the uneven bars (11,250) and couldn't build on her partner Kovtun's impeccable performance on the parallel bars (14,900).
Nagornyy only scored 13,850 after coming off the parallels but 2021 all-around world champion Melnikova made up for that on the final exercise, scoring 14.550 on the uneven bars for a total of 28,400 points against Ukraine's 26,150.