George Munsey – so often the man to provide impetus at the top of the order for Scotland – struggled to find the middle of the bat as he made 27 from 29 balls.
In contrast, Jones looked in magnificent touch as he found gaps in the off-side field and struck powerfully down the ground.
However, when Jones and Brandon McMullen (25) both fell in one Sompal Kami over, momentum evaporated.
Berrington (10) was the only other batter to reach double figures for Scotland as Tom Bruce, Matthew Cross and Leask all fell in quick succession.
Nepal’s bowlers used pace-off variations to great effect in the death overs with Kami (3-25) particularly impressive.
Mark Watt struck the final ball of the innings for six to boost Scottish hopes, but under lights on a good pitch it felt as though they were at least 10 runs short.
In reply, Nepal reached 56 without loss after a powerplay in which both openers were the beneficiaries of good fortune.
Brad Currie put down Kushal Bhurtel with a tough chance off his own bowling before Brad Wheal hit the stumps without dislodging the bails.
Wicketkeeper Cross also failed to cling on when Aasif Sheikh gloved one from Currie down the leg side.
Bhurtel (43) and Sheikh (33) were both dismissed by the ever-competitive Leask as Scotland fought back, and when the off-spinner also removed captain Rohit Paudel, Nepal were behind the eight ball.
That wicket brought Gulshan Jha to the middle with Airee in the 14th over and three sixes in consecutive balls off Olly Davidson and then Leask provided another twist.
Airee’s fast hands and faster running was the bedrock of the chase, as he rotated strike expertly and found the boundary when required to leave five required from six deliveries.
Having failed to take 10 from the final over in the defeat by England, Jha swiped Wheal for four through mid-wicket to seal a famous win for the team known as the Cardiac Kids.