After several missed chances in the first half, Brazil's Miranda finally broke the deadlock by tapping in a rebounded shot past goalkeeper Igor Akinfeev in the 53rd minute.
Philippe Coutinho doubled Brazil's lead with a penalty kick less than 10 minutes later. The playmaker's Barcelona team mate Paulinho quickly added another in the 66th minute, expertly heading a flawless cross by Willian into the back of the net.
Russia's best chance came just after the half hour mark with a drive from 20 yards by Spartak Moscow midfielder Aleksandr Samedov which was tipped over the bar by Brazil goalkeeper Alisson.
Akinfeev kept the Russian side afloat in the first half, making several key saves against a dominant Brazilian team.
The CSKA Moscow goalkeeper, known for his errors in major international matches, will have to play solidly if Russia hope to hold their own at the World Cup finals.
As the lowest-ranked team in the tournament, the hosts are hoping to make the knockout stage for the first time in post-Soviet history.
Russia have lost striker Alexander Kokorin and defenders Georgi Dzhikiya and Viktor Vasin to serious knee injuries since the start of the year, leaving manager Stanislav Cherchesov with gaps to fill in his line-up.
"It's clear that these are important players for us, but I think we need to wait and see how their recover," Cherchesov told a news conference. "We do not want and cannot cry over them. That is not in our plans and in our character because we have other players and that would insult them."
Brazil dominated possession from the start and manager Tite said his players' convincing performance, extending the side's unbeaten streak to eight matches, showed they are ready for the World Cup.
"Honestly I am very happy about our performance because we managed to do everything that was important to the game," Tite said. "We managed to score goals from different positions... the team understood what I want to see from them."
Russia take on France next week, while Brazil face Germany for the first time since their humiliating 7-1 loss to the Europeans on home soil in the 2014 World Cup semi-final.
The World Cup takes place from June 14 to July 15 in 12 venues spread across 11 Russian cities including Moscow, St Petersburg and Sochi.
(Editing by Christian Radnedge)
