Along with wicketkeeper Mohammad Ishaq, the pair got their team past 90, with Noor making a valuable half-century. England's crucial breakthrough came after some wonderful fielding led to a run-out for Ishaq with wicketkeeper Horton reacting quickly to a loose throw at the striker's end.
Noor remained stubborn but eventually went for 60, with Thomas Aspinwall claiming a vital wicket. That set up a frantic finish that could have gone either way.
The 44th over for England appeared to have turned the game when two no-balls in-a-row gifted their opponents eight runs, before Abdul Hadi (37 no) smashed a huge six to take them to 200 and tantalizing close.
But Ahmed's late flurry and a nerveless final over from Boyden carried England over the line to their first ICC U19 Men's Cricket World Cup final since 1998 in South Africa, when they lifted the trophy.