City had nine shots to West Ham’s five in an exciting first half, but a tally of just one each on target highlighted a lack of composure in front of goal from both sides.
The defences looked brittle under pressure too, and Shelina Zadorsky’s mistake in her own half resulted in the winning goal, as Vivianne Miedema broke to set up Fujino, who slid her finish across Kinga Szemik.
But despite their awful run of results and without a goal in their previous three outings, West Ham did not hide with a positive approach amid tentative defending from Andree Jeglertz’s side.
Ueki should have scored, but fired straight at the legs of her Japan team-mate Yamashita, while Asseyi blazed a volley wide following good work on the right from Ffion Morgan.
The busy Asseyi nearly made amends when she lifted the ball over Yamashita from close range, only to see her strike rebound off the crossbar.
City applied more pressure following that close call, with Shaw and Miedema thwarted by committed defending from Yu Endo, Oona Siren and Asseyi that typified West Ham’s performance without the ball.
Prior’s thumping header almost made it 2-0, while Skinner’s side repeatedly put their bodies on the line.
Despite extending their winning run, City will need to be more ruthless in front of goal if they are to maintain their title challenge as they could be punished by better sides.
West Ham will take heart from their competitive display but desperately need a first WSL point since April.
