Arsenal beat Crystal Palace 2-0, while Manchester United overcame Tottenham 2-1 to complete the semi-final line-up.
Laia Codina’s looping header put Arsenal in front after 20 minutes, but Renee Slegers’ side were unable to increase their advantage until Stina Blackstenius netted in second-half stoppage time.
Crystal Palace, the only Barclays WSL 2 side left in the competition, played in front of a record crowd of 3,040 at the VBS Community Stadium.
Meanwhile, after a thrilling 3-3 encounter between Manchester United and Tottenham in the WSL last weekend, United emerged victorious this time with a narrow 2-1 win.
Drew Spence opened the scoring for Spurs, but second-half goals from Jess Park and Fridolina Rolfo were enough for Marc Skinner’s side to progress.
Arsenal will host Manchester United in the semis, which will be played over 21 and 22 January.