In a fixture pitting two Premier League outfits against each other, it was the Redbacks who got off to the faster start as Tiana Botha shot wide in the opening 10 minutes.
Redbacks, who sit top of the Premier Division, broke the deadlock when forward Leota volleyed home after Carroll’s shot was blocked.
The goal was the only talking point of what was a cagey opening 45 minutes.
A pair of half-time substitutions by NTC coach Gavin Sit energised his squad as they went out in search of an equaliser – Abbey Green and Sarah Mitchell going close.
Those missed opportunities would prove costly as the Redbacks doubled their advantage just past the hour-mark when Bennett steered home Carroll’s indirect free-kick awarded after NTC goalkeeper Miranda Templeman had handled a back-pass.
Playing with confidence, Northern Redbacks added a third as Carroll scored from the penalty spot to send her side through to the cup semi-finals.
NTC went close to pulling back a consolation goal in the dying stages but Redbacks keeper Morgan Aquino produced a pair of quality saves to deny Green, while Leticia McKenna struck the woodwork with a thunderous free-kick.
Star player: Morgan Aquino (Northern Redbacks)
Northern Redbacks 3 (Leota 19min, Bennett 63, S Carroll 73) NTC Women 0
Celebration Park Sunday, 30 June 2019 Kick-off: 1pm Referee: John Westmurland Assistant referees: Arnold Mervis, Julian Putti