Paul Cudby's side took the lead through Jade Formaston in the 28th minute of the competiation which this year will have its final at Coventry's Ricoh Arena, and four minutes, Chris Torkidsen converted a penalty for the second.
Pope pulled one back for Wolves in the 58th minute and they equalised when Rebecca Large scrambled home to take the tie into extra-time.
Two minutes before the end of the first period, substitute Nicole Evans scored to put City to send City into the next round.