Chile's Mauricio Isla opened the scoring when he fired past Igor Akinfeev 11 minutes into the second half from a ball floated into the area by Alexis Sanchez, who had just come on.
But Russia, who are using the tournament to prepare for hosting the 2018 World Cup, equalised with a header by defender Viktor Vasin in the 67th from a Dmitry Kombarov corner.
Both sides failed to take their chances in the first period, with Chile midfielder Arturo Vidal's headed effort disallowed due to a foul in the box just before the interval.
South American champions Chile are fourth in the world rankings, while Russia have slipped to a record low 63rd.
The two teams are in different groups in the eight-nation Confederations Cup, a two-week World Cup warm-up event starting on June 17 that features European champions Germany amongst the continental champions and host country Russia.
The Russians will face New Zealand in the opening match, while Chile play Cameroon in Moscow on June 18.
(Reporting by Moscow Newsroom; Editing by Ken Ferris)
