Liverpool manager Juergen Klopp made nine changes to his side, giving starts to three teenagers, while his Italian counterpart Carlo Ancelotti opted for a largely full-strength Everton line-up.
Everton had the better chances, with Liverpool goalkeeper Adrian foiling goalbound efforts from Dominic Calvert-Lewin, Mason Holgate and Richarlison in the first half.
But the youthful Liverpool side played the more enterprising football.
Jones, a local-born academy product, delivered the killer-blow in the 71st minute with a superb curling effort into the top corner.
The defeat left Everton without a win against their rivals since October 2010.