Russia goalkeeper Igor Akinfeev made a string of fine saves to keep Russia level in the first half but was arguably at fault for Brazil's opener as he failed to keep a Thiago Silva header out of the danger zone, with Miranda on hand to turn home the rebound.
Within nine minutes Brazil had doubled their lead from the penalty spot with Aleksandr Golovin fouling Paulinho in the box as Coutinho stepped up to score.
Paulinho added his name to the scoresheet as Brazil moved through the gears, Willian hanging up the perfect cross for the midfielder to prod in at the far post.
Substitute Alan Dzagoev went close to grabbing a consolation for Russia, sending a drive narrowly wide as the match wound down.
Brazil created their first clear chance in the fifth minute with veteran defender Dani Alves sending Gabriel Jesus into the box with a well-placed pass, only for the Manchester City striker to slip as he shot and Akinfeev saved.
Coutinho's speculative long-range strike was plucked out of the air by Akinfeev as Brazil continued to probe.
Russia's first chance arrived in the 32nd minute, Alisson tipping Aleksandr Samedov's drive over the crossbar after Alves lost possession on the halfway line, allowing the hosts to break.
Paulinho should have given Brazil the lead shortly after the restart, but Akinfeev was well positioned, saving the Barcelona midfielder's shot with his legs after Willian teed the midfielder up in the box.
Having made a stunning but possibly accidental block with his face after Samedov deflected a shot directly at him, Akinfeev's mistake handed Brazil their opener in the 53rd minute.
The goalkeeper could only parry the Silva header directly fellow central defender Miranda, who slammed the loose ball into the roof of the net.
And when Paulinho was bundled over in the box by Golovin, Brazil made sure of their win.