The 32-year-old produced a typical poacher’s goal, tapping in from close range with what proved to be the winner six minutes before the break.
It was her 45th international goal, meaning she is now just one away from equalling Kelly Smith’s all-time England record of 46.
"It’s a dream come true," White said afterwards. "It’s weird because it’s come full circle – my first cap was against Austria and now my 100th. I just wanted the team to win.
"I love playing for England and scoring for England, so it's a dream for me."
Georgia Stanway was a second-half sub.
The win ensures England maintain their 100% start to World Cup qualifying, with five wins from five matches in Group D so far. Their next game is on Tuesday against Latvia.
Meanwhile, Hayley Raso played the second half of Australia’s 3-0 defeat at the hands of the USA.