The Reds are fifth in the table on 65 points after 36 games, one behind fourth-placed Manchester United, who have a game in hand over their rivals. Leicester are 19th on 30 points, two behind Everton in 17th spot with two games to go.
After a sluggish opening, Jones broke the deadlock in the 33rd minute with a superb first-time finish from Mohamed Salah’s cross after Leicester’s high defensive line was caught out by a long ball over the top from Liverpool keeper Alisson.
The 22-year-old midfielder put the ball in the net again three minutes later and once more it was Salah who set him up, with Jones taking a touch on the turn before rifling home.
The home crowd did their best to get their team back in the game but Alexander-Arnold scored a brilliant third after a free kick was touched into his path by Salah in the 71st minute and his thunderous finish into the top corner snuffed out any hope Leicester might have had of a comeback.
Liverpool bagged a seventh league victory in a row while Leicester have only taken two points from their last four games.
Additional reporting from PA