Inglethorpe and Yeguo brought further saves from Kingham as the Reds looked to be finishing the half firmly on top.
Frustratingly, though, Wolves found a way back into the contest a couple of minutes before the break, Clive Oduor putting a loose ball into the back of the net rather out of nowhere.
The second half started as a tighter affair and Wolves were level by the hour mark. Again it was somewhat out of the blue, an effort from Dapo Anunlopo finding the corner.
Wright saved twice from the dangerous Anunlopo as the hosts looked to complete the comeback, while substitute Coxon blazed over for the Reds from another good Garin centre.
Inglethorpe headed a Charlie Huth cross wide and Luca Eden teed up Coxon for an attempt that lacked real power.
Liverpool’s skipper then produced a superb shot that the goalkeeper tipped around the post – but from the subsequent corner, the Reds found a key third goal.
The initial cross was returned low into the middle by Inglethorpe and Coxon was there to control and find the net.
Deep into injury time, Inglethorpe crafted the best moment of a superb match, launching his shot over the goalkeeper from near the centre-circle after the Reds won back possession.
**Team**
Liverpool: M. Wright, Garin (Ekiugbo, 77), Owen (Murray-Holme, 70), Conde, Clarke, Hickman, Phillips, Huth, Farkas (Eden, 60), Inglethorpe, Yeguo (Coxon, 46).
Unused subs: Hilditch, Moran.
Goals: Inglethorpe (17, 90+6), Farkas (29), Coxon (87).
**Next up**
Liverpool are next in league action on Saturday September 12, hosting Burnley at the Kirkby Academy. Kick-off that day is 11am BST.