After a goalless first half, Miranda opened the scoring at the Luzhniki Stadium, which will host seven matches at this summerâs tournament including the final.
Philippe Coutinho scored a penalty for Brazilâs second before Paulinho headed in a third from close range.
Five-time world champions Brazil are now unbeaten in eight games.
They showed no sign of missing Paris St-Germain forward Neymar, who faces a race against time to be fit for this summerâs tournament after undergoing surgery on an injured right foot.
Brazil dominated the first half but it wasnât until after the break that they broke the deadlock, when Inter Milan defender Miranda slotted home a rebound after Russian goalkeeper Igor Akinfeev made a good save.
Paulinho was pulled down in the penalty area by Aleksandr Golovin, with Barcelona team-mate Coutinho coolly scoring the spot-kick for his ninth international goal.
Midfielder Paulinho then found himself unmarked to head home Willianâs cross.
Brazilâs next friendly is against Germany on Tuesday in Berlin, while Russia face France in St Petersburg.
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