De Leede took five wickets before smashing a remarkable 92-ball 123 on Thursday as the Dutch overhauled their 278-run target inside 43 overs.
The number of overs bowled was significant as, to climb above Scotland in the qualifying table, the Dutch needed not only to win but to do so with at least six overs to spare.
De Leede produced a stunning late flurry to carry his side to victory, completely eclipsing Brandon McMullen's century for Scotland earlier in the match.
His first one-day international century concluded with a run out with only two needed to win.
The Netherlands now go through to this autumn's showpiece in India alongside qualifying tournament winners Sri Lanka.
"We had a look at where we wanted to be at the halfway point, and from there you've got to do it," said De Leede.
"It was 10,11 an over, so for us it was about going into T20 mode. We tried to take as many runs as possible in each over and just see where we would end up.
"It's amazing, I can't describe the feeling, and it will be one big party tonight."
The Dutch qualified despite not being able to field several key players who were engaged in domestic county cricket in England. It is the first time they have reached the first World Cup since 2011.
Scotland beat three Test-playing nations in West Indies, Zimbabwe and Ireland, all of whom will also not be in India, but could not get past their fellow associate nation.
Their captain Richie Berrington told Sky Sports: "A really tough one to take. The guys are hurting."
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