Alan McCormack's EFL Youth Alliance South-East Division champions took an early lead through Oli Lynch, but saw the visitors lead 2-1 before Millar Matthew-Lewis headed in an equaliser on the stroke of half-time.
Kian Best's stunning strike proved enough, however, to edge a second half to see the Lancashire side through to a quarter-final with Southampton or Fulham.
Town started brightly, the impressive Jayden Luker creating the first chance of the game, bursting into the left side of the area in the seventh minute to cross low towards Oli Lynch, but Preston keeper Tommy Davis managed to intercept.
Luker was at the heart of all the early Town attacks, driving forward again - this time through the centre of the North End half - only for Davis to dive low to his left to save, with Lynch lurking once more ready to pounce on any spillage.
That was something he managed in the 17th minute when Luker fed Jacob Vickers to shoot, and Davis could only parry with Lynch quick to control, swivel and turn the ball in from two yards out.
Preston were level eight minutes later when Kitt Nelson's shot looped up just under the crossbar, and Felipe Rodriguez-Gentile stooped to head into the corner as the ball came down with keeper Sam Bentley unable to hold.
Town came within a lick of paint of regaining the lead four minutes before half-time when Luker once again engineered himself some space on the left edge of the area and pinged a low cross in that Millar Matthews-Lewis controlled instantly, before drilling a right-footed shot against the post.
The visitors gained the advantage with 45 minutes on the clock when Finlay Cross-Adair stabbed home after Joe Johnson had attempted to clear Rodriguez-Gentile's flick on from a corner.
But Town were deservedly level again inside the two minutes od added time when Matthews-Lewis headed Archie Heron's cross home emphatically at the far post.
Preston took control again just after the hour when they caught the Hatters out with a short corner routine on the right, with Jacob Slater rolling the ball back for Kian Best to strike into the top corner from 22 yards.
The Hatters had struggled to create any chances in the second half until the 78th minute, when Heron got to the right byline and fired the ball across the six-yard box, only for it to elude Lynch and substitute Jamie Odegah and pass right through.
Fellow sub Jack Lorentzen-Jones was next to drive towards the byline, this time on the left, as the Hatters started to ask questions. But once again Preston cleared and stood strong, with man of the match Burger then frustrated to see his 88th minute shot from just outside the box fly high over the bar into the Kenny End.
Lorentzen-Jones was soon tricking his way into the box again in injury-time, firing another low cross in that Preston cleared, with Luker seeing a shot blocked from the resulting corner as time ebbed away for the young Hatters.
Town: Bentley, Pinnington (c), Johnson, Burger, Bateson, Vickers, Martucci (Lorentzen-Jones 77), Luker, Lynch, Heron, Matthews-Lewis (Odegah 69). Subs not used: Hemlin, Odell-Bature, Moffat, Giwa, Hockey (GK)
North End: Davis, Wallbank, Slater, Kamara, Taylor, Best, Seary, Mawene, Cross-Adair, Nelson (Horan 90), Rodriguez-Gentile (Wilson 79). Subs not used: Pemberton, Pradic, Pasiek, Eccleston, Havard.
Goals:
LT - Lynch 17', Matthews-Lewis 45+2'
PNE - Rodriguez 25', Cross-Adair 45', Best 61'
Att: 928
