England had trailed to an early Andressa Alves penalty but equalised through Ellen White shortly after the break before Mead's long-range effort grabbed the points with 16 minutes to go.
It was an impressive recovery from Phil Neville's side who face further games against the United States and Japan in the four-team tournament as they continue preparations for this summer's World Cup in France.
But Neville will have been far from happy with some of his side's defensive sluggishness, which contributed to them falling behind in the 15th minute.
An error by Steph Houghton was seized upon by Marta and the Brazilian star surged into the box where Lucy Bronze was rather harshly adjudged to have barged her over.
Alves sent Chelsea goalkeeper Carly Telford the wrong way from the spot and Brazil were relatively comfortable holding onto their lead despite half-chances for Nikita Parris and Fran Kirby.
England started the second half with much more purpose and were level within four minutes when Birmingham striker White steered a low left-foot shot across Brazil keeper Aline after being played in by Kirby.
Parris could have put England in front after surging into the right side of the Brazil box only to fire straight at Aline instead of squaring for White, who lurked unmarked in front of goal.
But Mead made up for that error of judgement less than 10 minutes later when she picked up the ball outside the box on the right and, spotting Aline off her line, smashed home a rising effort from a tight angle.
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