The deadlock between the Premier League Southern Division rivals after half an hour, as Avilla Bergin's cross was turned in by Bianca Baptiste.
Wendy Martin was brought down in the area 5 minutes before the break and got to her feet to convert from the spot.
It was 3-0 soon after the restart, Martin supplying the cross for Bergin to score at the far post.
There was no further scoring until the last 7 minutes, when Ronell Humes not only got her first senior goal for Spurs but then set up Bergin to slot home her second of the night.
Tottenham may now face a repeat of last season's final against holders Charlton Athletic, who host Herne Bay in the second semi-final on Thursday January 28th.