Katerina Svitkova's goal was the first West Ham have scored in the WSL since Olli Harder took over as manager just before Christmas
Bristol City remain two points adrift at the bottom of the Women's Super League after a draw at West Ham.
Emily van Egmond's own goal put the Robins ahead after keeper Mackenzie Arnold missed a corner and the ball deflected in off her team-mate.
Katerina Svitkova levelled with a low shot from six yards shortly after half-time when City failed to clear.
Ebony Salmon earlier hit the post and City were denied a winner as Jemma Purfield's free-kick hit the bar.
City remain bottom on six points with West Ham two points above them with a game in hand.
It was a return to Dagenham for former Hammers boss Matt Beard, who is in temporary charge of the Robins with Tanya Oxtoby on maternity leave, but despite his side having the best chances they could not defeat his successor Olli Harder's side.
Grace Fisk had a looping header saved for the Hammers before Salmon hit the post for City.
Svitkova's equaliser came during a period of Hammers ascendency, although Salmon - who impressed throughout - nearly restored the lead for City when she broke down the right, but her weak shot was saved.
Sophie Baggaley kept City in it when she brilliantly tipped over Laura Vetterlein's 64th-minute free-kick, before Carla Humphrey had an effort cleared off the West Ham line.
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