After an opening 45 minutes which saw little goalmouth action, the deadlock was broken just after the hour mark when a Chloe Burr lob deceived the Hammers goalkeeper, with Bianca Baptist tapping the ball into the empty net.
West Ham pushed for an equaliser and were rewarded in the 75th minute when Stacey Little rose highest to nod home Jess Barling's free-kick.
Both teams pushed for a winner but neither were able to find the net.
"1-1 was a fair result. I thought both sides worked hard for the point," said Spurs Ladies manager Karen Hills after the match.
"From our point of view, it was a better all round performance and I hope this will kick start our season.
"We have a long trip to Yeovil this Sunday where we are hoping to pick up our first league points."
Team: Ayre, Pittuck, Downie, Smith, Schillaci, Maloney, Cheesman, Mcevoy, Martin (Chloe Burr 60), Baptiste, Wilson (Kirsten Thompson 75).