Clarke scored with nine minutes remaining to complete a comeback started earlier in the second half by Jill Scott, who cancelled out the opening goal by Sarah Gregorius.
England now sit second in Group B and remain on course for a place in the quarter-finals.
Hope Powell’s side were desperate for a win having opened their campaign with a 1-1 draw against Mexico, but found themselves trailing after 18 minutes in Dresden.
Amber Hearn played the ball across the box for Gregorius, who squeezed between two defenders to prod home from a few yards out.
England raised their tempo in the second half and their pressure finally paid off after 63 minutes with Alex Scott providing a perfect cross for namesake Jill to head home.
A second goal followed nine minutes from time from substitute Clarke. New Zealand goalkeeper Jenny Bindon attempted to punch the ball clear but it fell to Katie Hoyle, who laid off to Clarke for the striker to fire into the roof of the net.