With the tie ending in a 1-1 draw after 90 minutes, the Reds received an extra point for prevailing in the spot-kicks.
Goalkeeper Fran Kitching was the hero as she saved from Remi Allen in the shootout while captain Sophie Bradley-Auckland netted the decisive penalty.
After Sunday’s 2-2 draw with Reading in the Women’s Super League, Reds boss Vicky Jepson decided to give her squad players a chance with Kitching, Leandra Little and Yana Daniels handed a place in the starting XI.
After a goalless first half at Adams Park, the home side nearly took the lead when Fara Williams saw her effort strike the bar.