The Manchester City striker's goal, her fifth at this tournament and sixth overall, broke a tie with Kelly Smith and also moved her level at the top of the scoring charts with the United States' Alex Morgan.
She is also only the second England player to score in four consecutive appearances at a World Cup after Gary Lineker did the same between 1986 and 1990 but is the first to do it in the same competition.
Jill Scott gave England the lead over Norway in just the third minute sliding home after good work from Lucy Bronze and a slight miscue from White.
But White made it up for it just before the break in Le Havre finishing off a well-worked team move involving captain Steph Houghton, Bronze again before Nikita Parris slid across leaving an easy finish.
A semi-final with either the holders USA or hosts France awaits the winners.
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