The Rebels were dominant throughout but the home side missed some clear chances in the first half, and were made to pay.
With just four minutes played, Gavin James registered his first goal for the club as he ran onto Warren Harris’ through pass and slipped the ball between Harvey Rivers’ legs.
Cirencester missed a glorious chance to equalise soon after, with Charlie Griffin's shot skimming the outside of the post, and later spurned a number of half chances.
James volleyed over the bar after a long throw fell to him at the back post, and Harris went closer as his volley into the ground produced a good save from Rivers.
Simon Dunn also went close when he fired just over following good work from Harris to keep the ball in play and pull the ball across goal.
As the first half drew to a close, Slough had Mark Scott to thank for superbly tipping away a free kick from 25 yards out.
Slough piled on the pressure in the second half and had claims for a penalty waved away early on.
But it was Cirencester who scored the next goal of the match, with Griffin equalising for the hosts. Scott came out but was unable to clear the danger following a poor attempted backpass, and Griffin scored into an open goal from a wide angle.
Four minutes later though, Slough were deservedly back in front with Lewis Putman finding space to fire home.
And with ten minutes remaining, Gavin James added his second goal of the game to give Slough a larger cushion. Rivers missed the ball as he looked to claim a cross from Harris, and James' header came back off the near post and rolled along the line before eventually creeping in.
The Rebels made changes and there was still time for Rivers to save superbly from Putman and substitute Charlie Moone to have a goal ruled out for a debateable handball decision, however Slough had done enough to record another confidence-boosting three points.
Cirencester Town Line up
Harvey Rivers, Kyle Lapham, Aidan Bennett, James Coates, Matt Liddiard (c), Ben Brown, Chris Taylor, Adam Connolly, Charlie Griffin, Ollie Knight, Ross Langworthy. Subs: Lee Smith, Kalum Youngsam, Jody Bevan.