With 98 per cent of ballots counted on Monday, the Central Election Commission said United Russia had won nearly 50 per cent of the vote, with its nearest rival, the Communist Party, at just under 20 per cent.
Navalny was flown from Russia to Berlin last month after falling ill on a domestic flight in Siberia. Tests in Germany, France and Sweden found he was poisoned with a nerve agent.
The German government says tests in Germany, France and Sweden have determined he was poisoned with a Novichok nerve agent.
Moscow has denied involvement in the incident. The Russian foreign ministry said Germany's assertion was not backed by evidence and complained about the way Germany had chosen to release information about Navalny.
Sputnik V is named after the space satellite launched by Moscow in 1957.
Russian President Vladimr Putin emphasised that the vaccine underwent the necessary tests and has proven efficient, offering a lasting immunity from the coronavirus.
Russia has yet to conduct large-scale trials of the shot that would produce data to show whether it works - something immunologists and infectious disease experts say could be a "reckless" step.
Opposition politician Alexei Navalny had a different view and called the vote an illegitimate and illegal show designed to legalise Putin's presidency for life.
The government said athletes and coaches under contract with a Russian sports organisation would be put under medical observation and obliged to spend two weeks in quarantine upon their return to the country.
One of the more elaborate theories compares photographs of Putin over the years, claiming to have identified a number of different individuals posing as him.