Two tries in three first-half minutes by winger Jonny May helped Eddie Jones' side underline their World Cup credentials and gain a measure of revenge over the Wallabies who sent them packing from their own tournament four years ago.
Despite facing a daunting task against the All Blacks, who also advanced with a 46-14 demolition of Ireland, Woodward believes England can pull off an upset win when the teams meet on October 26.
"Never underestimate the value of momentum," Woodward, who led England to World Cup glory in 2003, wrote in a column for the Daily Mail.