Two goals in the opening seven minutes did the damage for Slough, who were slow out of the blocks once again, whilst the Rebels were guilty of missing a series of chances in the remainder of the game as Bedworth dug deep and protected their lead.
As early as the third minute, Bedworth captain Kyle Cartwright gave his side the lead as he rose to meet Luke Rowe's floated free kick, sending it past the returning Mark Scott and into the far corner.
Four minutes later, Slough's awful start continued with another mistake which let in striker Aaron Wint. He cut inside from the left and composed himself, taking full advantage of the time and space at his disposal, before bending a shot past Scott and into the other corner to make it 2-0.
Slough seemed shell-shocked by this, but almost immediately responded as Jamie McClurg was teed up for a strike outside the box, but Denham Hinds dealt with it comfortably.
The visitors grew into the game a bit more with Lewis Putman seeing a lot of the ball, but Bedworth almost extended their lead on 20 minutes as Daniel Creaney looped a header towards goal, but Scott tipped it past the post. Two minutes later, left midfielder Rowe burst forward into space and hit a long-ranger which Scott fumbled initially.
For the remainder of the half, Slough put pressure on the Bedworth goal and at times, forced the home side into desperate defending. Putman saw a free kick pushed over the bar, and from the resulting corner, Scott Harris' bullet header sailed over. The striker would later have to leave the action shortly before half time after suffering an injury, and was replaced by Charlie Mpi.
Putman was released and was one-on-one with Hinds two minutes later, but the striker was too slow to get a shot in, and was well tackled by Chad Degville-Cross. The Bedworth right-back was the hero again shortly after as he cleared a header from Gary MacDonald off the line.
Whilst Slough were getting in behind Bedworth on a regular basis, the final shot or cross into the box was thwarted, with the hosts getting numbers back to defend.
Half time saw another change for Slough, with Jake Parsons replacing McClurg as the Rebels looked for more attacking threat. Slough immediately went on the attack, and won a free kick which Putman again saw tipped over by Denham. Gary MacDonald side-footed over from Warren Harris' delivery as Slough continued to waste chances.
With an hour played, Bedworth's task became harder with the dismissal of defender Andy Westwood for a poor challenge on Adam Martin, leaving the Rebels with half an hour to find a way past the ten men.
But Slough struggled to create openings as they had done in the first half, and Bedworth's work-rate in closing down their opponents was maintained, which frustrated the Rebels. Slough could have fallen 3-0 behind after a rare break from Bedworth resulted in Rowe bearing down on goal, but firing wide of Scott's goal on his right foot.
Daniel Hicks was introduced for the final 12 minutes as a replacement for MacDonald, who suffered a cut to his head, and the recently-signed centre-half was immediately installed as a third striker to add some muscle to the attack.
With seven minutes left, Guy Hollis really should have pulled one back, but his free header from a corner went over the bar.
Slough eventually found a way past Hinds on 86 minutes as Hicks found the back of the net on his second debut for the club. He showed good composure to touch the ball past Hinds and slot the ball home from an angle to reduce the deficit.
However, in the time that remained, Slough were unable to fashion another chance and were left to rue missed chances and poor defending in the opening few minutes of the match.
Bedworth United Line up
Denham Hinds, Chad Degville-Cross, Luke Rowe, Andy Westwood, Kyle Cartwright (c), Nathan Haines, Ben Steane, James Jepson, Aaron Wint, Daniel Creaney, Richard Wesley. Subs: Alex Naughton, David Blenkinsopp, Mark Albrighton, Chris Tullin, Aaron Bains.