The Lyon star scored the third of the night with a clean, powerful hit that flew past Ingrid Hjelmseth into the back of the net.
Jill Scott gave the Lionesses the perfect start in Le Havre, converting from close range after Ellen White failed to connect after Bronze’s fine work down the right and smart cutback into danger.
White didn’t wait long to grab her goal though, doubling the lead on the stroke of half-time and Bronze made sure of the win before the hour-mark.
Nikita Parris failed to add gloss to the scoreline, seeing her spot kick comfortably saved by Hjelmseth.
England will now play France or the United States in the semi-finals.
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