It looked like Spurs' efforts were going to be thwarted when Romena Pinner struck for West Ham to make it 1-1 with only seconds remaining of the FA Women's Premier League encounter at Cheshunt.
Undetered, Spurs came forward again and Wendy Martin was there to head home Sophie McLean's cross in the fifth minute of injury time.
Martin, such a key player, came off the bench for her second appearance after injury just after the hour and opened the scoring eight minutes later.
Spurs went close to adding to their lead before West Ham levelled against the run of play but Martin made sure the points went to the right home.
Although Spurs were in control of possession and territory, the first half was even in terms of chances created with the visitors coming closest to breaking the deadlock on 35 minutes when Pinner struck the crossbar after Chloe Morgan denied Whitney Locke. Alex Keown was also forced into a last-ditch block after Pinner broke clear.
At the other end, Maya Vio, Katie O'Leary and Bianca Baptiste all had sites at goal, Vio and Baptiste forcing goalkeeper Aditi Chauhan into action.
Baptiste was denied again by Chauhan at the start of the second half before Morgan produced a textbook one-on-one save as Locke threatened.
Below: Shannon Moloney challenges two West Ham players
The opener arrived on 68 minutes when Megan Wynne bravely challenged Chauhan and Katie Bottom to a high ball. Chauhan's punch clear fell to Martin who volleyed back into the open goal from 25 yards.
Spurs then had chances to put the issue beyond doubt. Wynne headed wide from Rosie Kmita's corner and Baptiste struck the post with a fine volley but they were then rocked as Pinner fired home the equaliser.
But rather then feel sorry for themselves, Spurs came forward again, Baptiste twisted and turned before rolling back for Sophie McLean to cross from the right and Martin made no mistake.
Spurs Ladies: Chloe Morgan, Sophie McLean, Alex Keown, Jenna Schillaci, Leah Rawle, Kelley Blanchflower (Wendy Martin 61), Shannon Moloney, Maya Vio, Bianca Baptiste, Katie O'Leary (Rosie Kmita 61), Megan Wynne. Substitutes (unused): Toni-Anne Wayne, Mollie Kmita.