The Russians, who started the competition as favourites, performed their technical routine to Russian Dance by Denis Garnizov, and came away with the top score of the day, 98.100.
That put them in a commanding position at the top of the leaderboard, with China in second place with 97.000, and Spain third with 96.200.
Svetlana Romashina, part of the Russian team, said they were pleased with their solid start.
She said: 'It was good, our coaches were very happy and our scores were high.
'We're really happy because all the elements were very clear, and we'll try to put in another strong performance tomorrow.'
The final stage of the competition is tomorrow when the teams will perform their free routines.