The ladies put the issue beyond doubt in the first half as goals from Maya Vio, Andra Marcoci and Avilla Bergin saw them 3-0 up after 35 minutes.
Enfield responded after the break and pulled a goal back but there was no question of a comeback as Spurs booked a place in the last four. Gillingham are also through, Carshalton Athletic take on Herne Bay and Charlton travel to Maidstone in the other quarter-finals.
Manager Karen Hills gave us this report. "We controlled the game from the first whistle and basically did the job in the first half.
"The first goal came on 20 minutes finished well by Maya Vio after a good combination between Wendy Martin and Avilla Bergin.
"Avilla set-up the second goal for Andra Marcoci, twisting and turning down her flank before cutting the ball back for Andra who got the ball out of her feet before firing home.
"Avilla then scored the third goal when she drove at the Enfield defence, cut onto her right foot and drilled into the top corner.
"We made a couple of changes at half-time with Chloe Bassett and Jade Skillen coming on and we continued to dominate but Enfield came into it a little more and pulled a goal back through a defensive mix-up.
"We just dropped off a little, perhaps became a little complacent but I felt we were always in control.
"A special mention to Lucia Leon who played out of position at full-back with Jenna Schillaci and Natalie Grafton both unavailable. She looked comfortable in the role, showed great distribution all night and was always ready to support in attack. She played really well."
The ladies next scheduled fixture is back in FA Women's Premier League action at QPR on Sunday week, December 7.
Spurs Ladies vs Enfield: Toni-Anne Wayne; Lucia Leon, Alex Keown, Natasha Smits, Sophie McLean (Chloe Bassett, 46); Wendy Martin, Shannon Maloney, Maya Vio; Andra Marcoci (Leanne Mabey, 60), Katie O'Leary (Jade Skillen, 46), Avilla Bergin. Unsued sub: Lauren Picton.
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