The result marks an incredible turnaround for Eoin Morgan's side, who were on the brink of elimination in the group stage until back-to-back wins over India and the Black Caps secured a semi-final showdown with Australia at Edgbaston.
And on Thursday the hosts showed exactly why they were pre-tournament favourites, dismissing Steve Smith's men for 223 and chasing down their target with 17.5 overs to spare, thanks in large part to a swashbuckling 85 from Roy that was only ended following an incorrect call from umpire Kumar Dharmasena.
Roy and Jonny Bairstow (34) put on an opening stand of 124 after Chris Woakes (3-20), Adil Rashid (3-54) and Jofra Archer (2-32) had done the damage with the ball, with Joe Root (49 not out) and Morgan (45no) combining to see England comfortably over the line.
Australia won the toss and opted to bat but lost Aaron Finch, David Warner and Peter Handscomb early on before rebuilding through Steve Smith (85) and Alex Carey (46).
But England kept up the pressure, combining an excellent bowling performance with some first-rate fielding to limit the scope of the revival, taking key wickets at vital moments.
That left a strong batting line-up to take up the mantle, but only the top four were needed to get the job done, with a Lord's final – England's first in a World Cup since 1992 – up next.