The visitors started brightly and took the lead inside the first five minutes when Rob Laney beat Rebels keeper Mark Scott to a bouncing ball and headed into the empty net.
Reece Beccles-Richards fired over the bar after finding some space in the Slough box, but halfway through the first period, the lead was doubled as the impressive Beccles-Richards held off Paul Stonehouse to fire in through the legs of Scott.
The second goal seemed to wake Slough up, with Lewis Putman forcing Shane Gore into a good save from a free kick before Lee Togwell drilled home from the edge of the box following a punch from Gore just after the half hour point.
The Rebels had much the better of the remainder of the first half but were unable to find the equaliser. Three minutes after scoring, Togwell was brought down on the edge of the box and Putman struck the resulting free kick across Gore’s goal but off the post. Shortly after, Togwell saw another effort well blocked.
Tempers flared at the end of the first half as Wingate & Finchley picked up their fifth yellow card as Sean Cronin, Claudiu Vilcu and Gore were all booked after an altercation with Charlie Moone.
Missed chances were to cost the Rebels, despite the home side dominating the second period.
Slough appealed in vain for a penalty and forced a series of corners, but could not capitalise on Putman’s deliveries.
Then, against the run of play, Ben Pattie’s well-taken strike from Laney’s cross restored the visitors’ two goal advantage.
Adebayo headed wide with Warren Harris in a better position, and Moone was thwarted by a low save from Gore as Slough pushed men forward. In doing so, the home side left gaps at the back and Beccles-Richards almost found himself through on goal, but was adjudged to have fouled Guy Hollis.
Slough were never at their best but breathed life into the game when substitute Gurkan Gokmen tapped in from Lewis Putman’s centre with two minutes remaining.
It was not to be though as Wingate & Finchley went straight up the other end and wrapped up the victory with captain Ahmet Rifat’s strike going in off the post. The already substituted Laney earned Wingate’s seventh caution in the celebrations but the visitors will not care too much as they progress to the First Round leaving the Rebels to focus on their league campaign.
Wingate & Finchley Line up
Shane Gore, Alfie Young, Ryan Sellars, Claudiu Vilcu, Sean Cronin, Ahmet Rifat (c), Steve Wales, Luke Ifil, Ben Pattie, Reece Beccles-Richards, Rob Laney. Substitutes: Tanasheh Abrahams, Max Kyte, Joe Sharpe, Cornel Flavia-Cornea.