Following a first half that saw the Selecao struggle to create too many clear-cut openings, they stepped things up early in the second half with a three-goal blast inside 13 minutes.
For all Brazil's attempts in the first half, racking up six on target alone, only once did they truly look like finding a way through at the ground that will host the opening game of this summer's World Cup.
Casemiro then had a shot kept out and Coutinho's curler from the edge of the box was also easily dealt with by Russia's 104-cap keeper.
Brazil continued to probe away in search of an opener, with Willian seeing three fairly tame efforts dealt with, but the hosts more than held their own in a defensive sense as they restricted their opponents mainly to long-range shots.
Russia, seeking a first win against Brazil in six attempts, may even have taken a lead into the break as Alisson twice kept out Aleksey Miranchuk, and the attacking midfielder also skied a chance from seven yards.
Eight minutes of the second half is all that the Selecao required to open the scoring, though, with Miranda firing home a rebound after Thiago Silva's header was parried into his path - international goal number two for the Atletico Madrid defender on his 44th cap.
The five-time World Cup winners had been knocking on the door for a few minutes before that opener, twice being denied by Akinfeev from Paulinho and Willian shots inside the area.
That dominance continued after the goal, and they were rewarded with a second through a Coutinho penalty after Aleksandr Golovin was penalised for pulling back Paulinho.
Paulinho, guilty of missing a close-range sitter earlier in the half, made it three soon after by heading home Willian's chipped cross.
Alisson was equal to Dmitri Kombarov's strike as Russia attempted to offer some sort of response, while Anton Miranchuk failed to convert from under the crossbar following a goal-line clearance from Silva in the final meaningful opportunity of the contest.
RUSSIA (5-2-2-1): Akinfeev; Samedov (Smolnikov 80'), Kutepov, Granat, Kudryashov, Kombarov (Zhirkov 76'); Glushakov (An. Miranchuk 64'), Zobnin (Erokhin 85'); Golovin, Al. Miranchuk (Dzagoev 53'); Smolov (Zabolotnyi 71')
BRAZIL (4-3-3): Alisson; Alves (Fagner 83'), Silva, Miranda (Geromel 86'), Marcelo; Paulinho (Augusto 71'), Casemiro, Coutinho (Fred 79'); Willian (Taison 79'), Jesus (Firmino 65'), Douglas Costa