England coach Hope Powell believes there is more to come from her side as they try to reach the last eight of the Women's World Cup.
Second-half goals from Jill Scott and Jessica Clarke were enough to defeat New Zealand 2-1 in Dresden.
After a disappointing draw in the opening game with Mexico, England now need a point against Japan to progress.
Powell said: "We are just glad we got through the game but there is more to come from us."
England were in trouble at half time after New Zealand striker Sarah Gregorius bundled in a close-range strike.
Powell brought on Karen Carney at the interval in a tactical reshuffle and England were much improved after the break.
Everton midfielder Scott headed in a leveller before Clarke drilled in a late winner.
"We were confident we could turn it around after a slow start," Powell told BBC Sport.
"We made some changes and told them to get the ball out wide and get Jill Scott and Ellen White into the box to put New Zealand under pressure.
"Kelly Smith went up front to hold the ball up and it paid off.
"The win will hopefully help us relax. The expectation was that we would come through the group but we are not there yet."
A point against Group B leaders Japan on Tuesday evening will be enough for Powell's side to secure a quarter-final against either France or hosts Germany.
Japan thrashed Mexico 4-0 earlier on Friday and will prove tough opposition for England in Augsburg, but goalscorer Scott is confident of a strong performance.
She said: "We've been watching Japan, who are a good team, but this tournament has not seen the best of us yet.
"Our aim is to get three points and our mindset is to beat Japan."