Goals from Ben Woodburn and Abdi Sharif drew the young Reds level after Conor Gallagher's two first-half finishes had put the visitors 2-0 up at the Academy.
And a brilliant effort from Jones then secured all three points in dramatic fashion.
Neil Critchley's side were caught off guard and fell behind inside three minutes, with Gallagher tapping in Tariq Lamptey's cross from the right.
Caoimhin Kelleher then saved twice - from Tariq Uwakwe and Joseph Colley - to stop Chelsea from adding to their lead in the ninth minute.
The dominance from the visitors continued.