Manchester United striker Press set her team on the path to victory with neat 11th-minute opener.
The second half saw a Marta-inspired Brazil desperately press forward in search of an equaliser, but they failed to find the target from several goal-scoring opportunities.
Super substitute Rapinoe eventually put the game to bed with a second goal on 87 minutes.
Reigning world champions the United States are now unbeaten in 36 consecutive games, and haven't lost against Brazil in their last seven meetings.
Alex Morgan returns
The game was extra special for US striker Alex Morgan, who started her first international since giving birth to daughter Charlie last year.
The USA beat Canada 1-0 in their tournament opener on Thursday.
Their latest victory means they take a giant step towards securing a fourth SheBelieves title, as they sit atop the standings with one round to go.
Third-placed Canada take on basement side Argentina later this evening in Orlando's Exploria Stadium.