They overcame a spirited display from Copsewood Coventry Ladies on Sunday to win 2-0 and to set-up a third round tie at home to Cardiff City, who play one step above Spurs in the FA Women's Premier League, National Division.
Davina Smith had an instant impact after coming off the bench to grab the opening goal against Copsewood Coventry.
Entering the action for Andra Marcoci in the 57th minute, Davina scored with her first touch from Jenna Schillaci's corner for 1-0.
Wendy Martin made it a quick one-two minutes later and at 2-0, it was all over against the team from the Midlands Combination.
"First of all, I've got to mention Lauren Picton, our reserve goalkeeper, who came in for Jo Ayre and made a fanatstic save when it was goalless in the first half," said manager, Karen Hills.
"It was a tough game, we went into it as favourites and we knew we had to do things right. We had a bad experience in the FA Cup against Larkhall in Somerset last season and didn't want that again.
"It was a bit of a slow first half, Lauren made that crucial save but they didn't really threaten and you always felt it was a case of when we'd score, we'd go on to win.
"We now face Cardiff in the third round. They play in the National Division of the Premier League and that will be a big test for us.
"We'll go in as underdogs for that game but we're at home and we'll definitely have a chance. Hopefully, we'll get a few Spurs fans along to cheer us on."
That match is scheduled for Sunday, February 3 with a 2pm kick-off at Harlow Town FC.
However, the ladies have a another big test before then, with leaders Reading scheduled to visit Harlow Town this Sunday, January 13, again at 2pm.
They top the Southern Division of the Premier League with seven wins in nine matches.
Karen added: "Reading were relegated from the National League last season, but they've held onto most of their players and they have a lot of experience.
"They are organised and again, it's a tough one for the girls but we're confident at the moment and looking forward to it."
Spurs Ladies v Copsewood Coventry - Picton; O'Halloran (Downie), Pittuck, Heath, Schillaci; Wilson, Cooper (Maloney), Martin, Cheeseman; Burr, Marcoci (Smith).