There were seven changes to the team that were beaten in the Merseyside derby, with the likes of Eartha Cumings, Hannah Silcock and Rachel Furness all coming into the lineup.
Defender Rhiannon Roberts was also due to start, but withdrew from the XI as a precaution, with Emma Koivisto replacing her.
Liverpool, who were wearing the club’s brand new green third kit, started well, with Katie Stengel sending an effort crashing off the bar in the early stages.
The breakthrough came when Yana Daniels was brought down on the edge of the box, before Campbell stepped up to fire her free-kick into the bottom corner.
Daniels had two big opportunities to double the lead before half-time, and there were chances for the likes of Silcock, Furness and Stengel in the second half, but Campbell’s free-kick was enough to secure the points.
Liverpool FC Women: Cumings, Koivisto, Robe, Silcock (Flaherty, 64), Matthews, Campbell (Hinds, 46), Furness (Holland, 84), Wardlaw (Kearns, 46), Humphrey (Lawley, 56), Daniels, Stengel.
Subs not used: Laws, Kirby, Fahey.