The Women's Super League game was played at Kingsmeadow.
The visitors were in front after two minutes.
Fran Kirby scored an equalizing goal before the half-time break.
Sam Kerr, who hit the post twice, scored the second goal for the home side, before Millie Bright's goal made it 3-1 to the visitors.
Lauren James won a penalty for the Blues, but could not beat Arnold from the spot.
Lauren was impressive again in a brief appearance from the bench.
She caused a lot of problems for the West Ham defence.
LucyParker, who earned her first England call-up on Tuesday, did well to keep her at bay but Kerr's quality was evident when she struck powerfully against the post.
The Australia international finally got her first goal of the season when West Ham failed to clear the ball in the box and it dropped kindly for her to poke in from close range.
Bright had a chance to score before the final goal, but he sent a shot wide.
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