The AC Milan star strikes twice after his fellow forward's opener to give under-fire coach Mano Menezes a much-needed victory in the wake of the nation's Olympic heartbreak
The venue, which is due to be demolished in November, was the site of the 1958 World Cup final in which the two sides went head-to-head; that game finished 5-2 to the Selecao but the rematch did not quite scale such prolific heights.
Leandro Damiao opened the scoring in the first half before substitute Alexandre Pato netted a late double to cap an impressive and commanding performance.
After Pele, who scored two goals in that 1958 final, had placed the ball for kick off, neither side forced itself on the other but Brazil held an advantage due to its far greater retention of the ball.
In the 18th minute, Neymar tapped home after an effort from Oscar had rattled the post. However, the assistant referee had raised his flag and dubiously declared the Santos man offside.
Sweden was offering very little going forward, with just Christian Wilhelmsson offering a positive, purposeful outlet. It could have been two up with 24 minutes played but although Alves' free kick had Andreas Isaksson beaten, it flew narrowly wide of the bottom corner.
Brazil continued to up the ante and after Thiago Silva fell narrowly short of a tap-in from Neymar's pass, Damiao added the finishing touch to the 20-year-old's next delivery. A wonderful ball in from the left was met by the in-demand Internacional forward, who headed in his second full international goal.
The Blagult, who had not created an opportunity all night, had two opportunities to equalize on the stroke of halftime. After some lovely interplay, Marcus Berg was denied by Gabriel and then, from the resultant corner, Andreas Granqvist volleyed wide of the goal.
Within 10 minutes of the restart Brazil could well have run away with the game. Alves had a booming shoot palmed away by Isaksson and moments later Neymar poked wide after attempting to be too clever. Damiao then completed a hat trick of missed chances as he found Paulinho's flick on agonizingly out of reach at the back post.
There was little Erik Hamren's men could do to resist the Samba Boys but some impressive organization was maintaining a single-goal difference between the pair. However, after some off-target attempts from Damiao, it was his replacement who managed to finish off the resilient Swedes.
Pato was brought on in the final 15 minutes and he polished off the win with two goals in quick succession. After tapping home Alves' little dink over Isaksson, the AC Milan striker won and converted a penalty in the 85th minute to give the scoreline the gloss it deserved.
Sweden sorely missed talismanic forward Zlatan Ibrahimovic and it will expect a much better result when he returns for its World Cup qualifier against Kazakhstan next month. Brazil, meanwhile, will be seeking further improvement when it continues its non-competitive fixture list with another friendly in September against South Africa.