Slough were missing Christian Metcalfe, Darron Wilkinson, Ian Hodges and Leigh Mason through injury and also had to delay the start of the match with Andy Ballard, Michael Alexis and Garath McCleary arriving late.
The visiting team started well and Gianni Frankis pulled Clark Masters into action when he ran onto a through ball and attempted to lift the ball over the keeper, but Masters stayed up well and was able to block the ball close to the edge of his area.
Ballard opened the scoring for Slough with just under twenty minutes played. Ballard laid the ball into the feet of Matt Seedel and continued his run. The forward returned the ball to Ballard and as it sat up, he jump kicked it over the head of Paul Nicholls and into the net.
McCleary leathered the ball into the bar next for Slough after an Alexis free kick had bounced back off the wall and Masters was well positioned to palm over a direct free kick from Alexis Charalambous which was heading towards the top corner.
Heybridge came into this cup quarter final in great form, having won their last six league games in a row, but Slough were dealing with them very comfortably as the first half came to a close.
The visitors certainly started the second half with a renewed vigour and had the better of the opening exchanges, but apart from a Gianni Frankis flick which lacked power and was stopped by Masters just in front of the line, Slough remained comfortable.
The home side should have extended their lead when a pass out from Nicholls to was miscontrolled by Artun Erdem and McCleary and Ballard pounced with the latter feeding in the former but unfortunately he could only shoot wide of the near post.
Slough did extend their lead in the sixty third minute. A right wing corner from Glen Harris was controlled by Ballard. His first touch took him away from goal into a bit of space and he was able to hit a low left footed shot which found it's way under the hand of Nicholls and into the net.
Ballard completed his hat trick three minutes later with Harris again the provider. A free kick from just outside the right hand side of the area was flicked on at the near post by a defender then met by a looping header from the midfielder which went over Nicholls and dropped in under the bar.
Heybridge nearly got one back as Neil Cousins challenged Masters which saw the keeper spill a high ball and the visiting striker then headed goalwards but with Mark Avery covering the ball went wide of the post.
Slough saw the game out comfortably and progressed through to the semi finals for the second season running in the hope of retaining their League Cup title.
Heybridge Swifts Line up
Paul Nicholls, Erdem Artun, Ian Cousins, Alexis Charambalous, Paul O'Donoghue, Danny Barber, Russell Pond, Paul Abbott, Sean Marks, Gianni Frankis, Neil Cousins. Subs: Ian Wiles (for O'Donoghue), Steve Spencer, Simon Glover, Mike Shinn (for Pond), Adam Gillespsie