Aylesbury deserved their win on the balance of play as although Slough had slightly more of the ball, their opponents made the more threatening chances when they had it.
Nando Perna, Enzo Silverstri and Kevin Mealor all had chances for the visitors before Terry Davies had Slough's opening chance after fifteen miniutes as he shot wide of the far post having been set up by Mark Bartley.
Bartley was next to fire wide for the Rebels, with his curling effort going just wide before Davies again went close, this time finding the target, but also finding Tom Vincent in the way.
United took the lead in controversial circumstances. Having a brief spell of pressure, which saw Richard Pringle's header well saved by Drake, Pringle then headed home Mealor's cross whilst appearing to be a few yards offside. To the astonishment of just about everyone, including the goalscorer, the goal stood and Aylesbury were in front.
The lead only lasted two minutes as Matt Miller brought the Rebels back onto level terms soon after. A long throw from Stevel Dell was misjudged by Carl Kavanagh as it bounced up over the defender allowing the ball to arrive at the feet of Miller. The striker turned his way past Nathan Liburd and shot over the dive of Vincent and in at the near post.
Aylesbury were back in frontbefore the half was out with Pringle again getting on the scoresheet, this time in much less controversial circumstances. A long ball forward was flicked on by Leon Gutzmore into the path of Pringle who ran through and slotted home with his left foot.
Slough did press for an equaliser, but as has been the case often this season, they were able to offer little upfront, despite a lot of effort.
Perna, Pringle and Daniel Mead all had opportunities with only the latter needing a save from Drake as Aylesbury looked the more likely to score.
Davies fired off target and Steve Dell put a header over when well placed after Vincent hadn't got a decent connection with a punched clearance.
Slough were getting the upper hand in the game but were now beomcing increasingly desperate and lacking in ideas. Their attempts at slowly building up play ahd gone in favour of a more direct approach and this was being easily defended.
Leigh Mason had two chances in the conclusion of the game, with the second in particular bringing a save from Vincent, but was far too close to the keeper.
Aylesbury held on and progress into the Quarter Finals where they will face Wycombe Wanderers.
Aylesbury United Line up
Tom Vicent, Nathan Liburd, Kevin Mealor, Carl Kavanagh, Nick Leach, Liam Smyth, Daniel Mead, Enzo Silvestri, Richard Pringle, Leon Gutzmore, Nando Perna. Sub: Luke Melisi, Matthew Butler, Justin Gordon, Kyle Kilmartin, Daniel Jones.