The England and Barcelona defender went down with the game tied when USA's Hailie Mace sent a high boot into her face as the visiting side tried to clear their lines.
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It was a dramatic first half as the European champions faced the reigning World champions, with Lauren Hemp's opener being cancelled out by the USA's Sophia Smith.
But just a few minutes later, controversy struck as Bronze went down injured.
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The European championship was left on the floor clutching her face, as referee Riem Hussein allowed play to continue, leaving England fans and the England bench furious.
Then, after the US had tried to attack, VAR intervened, and Hussein went over to the monitor.
After a brief look, the German official awarded England a penalty, much to the delight of the sold out Wembley crowd as the Lionesses looked to regain their lead.
But Mace was only awarded a yellow card, despite replays showing her boot making direct contact with Bronze's face.
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Cool as you like, Stanway converted the penalty, sending the ball into the bottom right hand corner, securing the matchwinner.
England then thought their redemption had been undone when Trinity Rodman found the net not long after England went 2-1 up.
However, after another VAR review, the goal was narrowly chalked off for offside.
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But for former England star Ian Wright, the officials made the wrong decision.
"This is not what VAR is for," he said on ITV, "This is ridiculous. How can they be disallowing these kind of goals man?"