Captain Casey Stoney set them on their way with a close-range finish in the 18th minute, with Jill Scott adding the second five minutes later.
Steph Houghton, the heroine of the opening win over New Zealand, sealed the win with her fierce strike eight minutes from time.
And with Brazil and Britain having recorded two wins from two, both sides are guaranteed a last-eight berth ahead of their meeting at Wembley on Tuesday.
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