Georgia Stanway released White to slot home the opener in the 14th minute, and the same player wrapped up the win six minutes from time.
A much-changed England were already through to the knockout phase before this, but the victory in Nice ensured that they progress as winners of Group D. It also allowed them to gain a measure of revenge for their heartbreaking 2-1 defeat against the same opponents in the semi-finals four years ago.
"We've got another clean sheet, we've won another game, we've played three and won three, and we're just where we want to be, in the last 16, and ready to attack the business end of the tournament," said Neville.
White came back into the line-up as one of eight changes following the 1-0 win over Argentina, and took her tally of goals in this World Cup to three overall.
"I'm delighted to have got two starts and for me I am delighted to contribute to this team in any way I can, on and off the pitch, and contributing with two goals is a dream really," said the 30-year-old.
"It was about winning the group, that is what we have done and now we will look forward to the round of 16."
While both sides were already through before this encounter on the Cote d'Azur, there was certainly plenty to be gained by finishing first in the section given what is likely to come next.
Having arrived in France with genuine ambitions of winning the trophy, England will now head north to Valenciennes for a last-16 tie on Sunday against a third-placed side from another group.
However, they will not know until late on Thursday who they will be coming up against, with Cameroon, New Zealand, Chile and even Thailand all potential opponents.
The permutations are less complicated for Japan, but the Nadeshiko - World Cup winners in 2011 and runners-up in 2015 - will surely have a stiffer test in Rennes against either the Netherlands or Canada.