Andre Onana misjudged the flight of Neco Williams‘ cross and 19-year-old midfielder Jones took advantage to score with the outside of his right foot.
Caoimhin Kelleher, deputising for first-choice keeper Alisson who was missing with a hamstring injury, also played his part in Liverpool’s win, a one-handed stop to deny Noussair Mazraoui the pick of his saves.
Jones also rattled a post before his goal ensured Liverpool, with one game to spare, joined Premier League rivals Manchester City and Chelsea in the knockout stage.
Kelleher impresses in Alisson’s absence
A surprise home defeat by Atalanta last week had threatened Liverpool’s dominance in Group D, with the Italians and Ajax closing in.
But Jurgen Klopp’s side overcame their latest worrying injury setback to progress after an open and entertaining game at Anfield.
It was far from straightforward for the Reds, Klaassen heading wide for Ajax when he should have scored, while Neres was denied by the woodwork after Kelleher had done well to push away an attempt by young Brazilian forward Antony.
The 22-year-old’s stop to deny Huntelaar, having earlier produced a one-handed save to keep out Noussair Mazraoui, was exceptional and at the final whistle, Klopp went straight to the Republic of Ireland squad member to congratulate him on his performance.
With Atalanta held in Denmark by Midtjylland, Liverpool are four points clear with one game to go and uncatchable at the top.
Having already secured the group, Klopp will be able to rest players when the Reds face Midtjylland in Denmark in the final round of games on 9 December.