In a match that was initially reduced to 23 overs per side in Aberdeen, Alastair Cook led his side to a comfortable victory on the Duckworth-Lewis method.
The players were off the field shortly after and the wet weather cost each side another three of their allotted overs, prompting Eoin Morgan to be promoted up the order and contribute a quickfire 31.
Cook, who made 44 from 47 balls, and Jos Buttler (9), fell before Morgan was caught behind off Ian Wardlaw with the scores on 140, and two wickets in the final over from Josh Davey restricted England to 167-7.
The new-ball pairing of James Anderson, who was recalled to the one-day side by Moores and picked up two wickets, and debutant Harry Gurney, kept things tight and immediately put Scotland behind the rate.
Leask was caught on the boundary off James Tredwell and Scotland quickly folded from 95-4 to 111-9, with a 22-run stand for the final wicket nowhere near enough to take them close to their target.
Tredwell finished with 4-40 from four overs as Moores made a winning return to the international scene.