This was a desperately poor performance from the Rebels, who have now won just one of their last eight matches, and were frustrated on a number of occasions by Ardley goalkeeper Jack Harding.
Slough handed full debuts to the central midfield duo of Adrian Sear and Ryan Scott, with Sean Fraser covering for Ryan Parsons' absence at left-back, whilst Scott Harris partnered Ed Smith in attack in the absence of the ill Johnnie Dyer. Guy Hollis returned to the team following injury.
Neither side started particularly strongly in a cagey opening quarter of an hour, though Harding made the first real save of the match, diving quickly to his left to turn away a first-time effort from George Frith.
The visitors scored the opening goal to stun the Rebels on 28 minutes. Ardley won the ball in midfield and Luke Ingram ran through on goal, placing the ball between Jake Somerville's legs and into the net.
Sluggish Slough struggled to break through the Ardley defence, Frith putting a shot wide from the edge of the box after intricate build-up play.
Smith later had a shot blocked after linking up well with Frith again, and had the ball in the net after Harding parried a long-ranger from James Dobson, but he was in an offside position and the goal was disallowed.
The visitors pressed Slough all over the pitch to good effect, with the Rebels rushed into mistakes on numerous occasions. Slough did, though have a glorious chance to level the scores just before the break, but Smith fired straight at Harding after breaking into the box.
Five minutes into the second half, Slough were awarded a dubious penalty as Smith was felled, and this time the Rebels were able to equalise, with James Dobson smashing in the penalty to score his fourth goal of the season.
Neil Baker and Jon Underwood freshened up the attack with Darryl Thomas and Adam Cornell replacing Scott Harris and Ed Smith, both short of fitness, but Slough still looked disjointed.
Reece Yorke was denied by Harding as his bullet header looked destined for the net, and then Ardley regained the lead. Somerville made a save from a corner, but Gavin Kidd was on hand to put the ball into the net from close range at the second attempt.
Looking for an immediate equaliser, Cornell was unlucky to see an effort fly over the bar from close range.
The best chance to force a replay came and went as Cornell's shot was saved by the impressive Harding, but Dobson sliced the rebound horribly wide with the goal gaping.
Slough threw forward Reece Yorke and Tom Moran as the game moved into stoppage time, but Ardley held on to secure a deserved win which moves them into the Second Round Qualifying.
Ardley United Line up
Jack Harding, Gavin Kidd, Harry Brock, Callum Convey, Chris Jackson, Tommy Kinch, Darren Beckett, Ollie Stanridge (c), Ricky Johnson, Luke Ingram, Joe Eyre. Subs: Adam Beckett, John Gardner, Kieran Scott.