Fern Whelan grabbed the Magpies' third in a comfortable 3-1 victory.
Birmingham City Ladies are into the next round after strikes from Andrine Hegerberg and Melissa Lawley earned a 2-0 win against Oxford United Women.
Goals from Leandra Little and Lauren Cresswell gave Doncaster Rovers Belles a 2-1 win over Sunderland Ladies.
England striker Ellen White scored twice as Notts County Ladies beat WSL 2 leaders Yeovil Town Ladies in the Women's Continental Cup first round.