Elise Thorsnes had given Norway the lead in the 56th minute, but Simon tied it just a minute later. Her powerful header from Kim Carroll's corner kick then sealed the win in the 87th.
Before 18,474 fans at the Bay Arena, neither side created any clear-cut chances before the game came to life when Thorsnes capitalized on a defensive mixup to open the scoring.
Norway defender Trine Ronning hit the crossbar with a free kick in the 84th.
Norway needed to beat Australia to advance from Group D. It's the first time the team failed to advance from the group stages at the World Cup.