They moved a point ahead of the Hammers thanks to a draw against fourth-placed Cardiff City Ladies on Sunday.
West Ham have one match remaining - a trip to FAWPL leaders Portsmouth on Sunday - while Spurs travel to Copsewood Coventry on Sunday before their finale against QPR at Ware FC on Wednesday week, May 13.
It was a familiar tale again against Cardiff as the team were denied maximum points by a late equaliser.
Eartha Pond registered her first Spurs goal to open the scoring in the first half, Naomi Clipston levelled for Cardiff with 20 minutes remaining only for Wendy Martin to convert for 2-1 after Eartha's free-kick came back off the post.
However, with eight minutes left, Laura Williams curled home a free-kick for 2-2, and that's how it stayed.
"We played well again but conceded late again, so that was disappointing for the girls," said manager, Karen Hills.
"We've two games left now and we're determined to finish fifth. It's been a superb season, our best yet and we just want to finish it off now.
"We've progressed again and we're already looking forward to next season. As we've found out this season, we can compete with the best at this level and it's just a case of ironing out some of the smaller details and we can progress again."
Meanwhile, it's worth noting that WSL 1 team Notts County Ladies, who beat Spurs Ladies in the fifth round of the Women's FA Cup back in March, have reached the final after toppling Everton Ladies at Goodison Park. They will play Chelsea at Wembley in August.
Spurs Ladies vs Cardiff: Toni Ann-Wayne; Eartha Pond, Jenna Schillaci, Sophie McLean, Lucia Leon; Maya Vio (Mollie Kmita, 81), Shannon Maloney, Wendy Martin; Leah Rawle (Avilla Bergin, 60), Katie O'Leary, Bianca Baptiste (Rosie Kmita, 70).