The 18-year-old Melnikova, the one remaining member of the team that won the title in Berne 2016, spearheaded a successful defence alongside Irina Alekseeva, Liliia Akhaimova, Uliana Perebinosova and Angelina Simakova.
Melnikova and another 18-year-old, Frenchwoman Melanie de Jesus, were the day's outstanding performers at the SSE Hydro Arena but it was the overall strength of the youthful Russian quintet that proved the key as they won with some comfort.
The Russians' total of 165.195 was more than four marks clear of silver medallist France's 161.131, in which De Jesus contributed the day's best individual total of 56.266. The Netherlands team won bronze with 159.563.
Akhaimova was the eldest in the Russian team at 21 but it was the sterling performances of 15-year-old Simakova, Alekseeva (16), Perebinosova (17) and, above all, Melnikova which continued to suggest the brightest of futures for Russian gymnastics.
Every one of the 12 routines by the Russian quintet scored more than 13 marks with Melnikova, the national all-around champion and member of the silver medal-winning Olympic team from 2016, being awarded two 14-plus marks on the vault and uneven bars.
Melnikova, who has the chance to add three more medals in Sunday's apparatus finals, was particularly delighted after the team had only been able to finish second to the French in qualification.
"It feels great. Qualifications were a bit stressful, but of course we all helped each other, the team was very united and today we managed to overcome all our difficulties," she said. "We're happy and we have no words."