Slough were impressive throughout, but it took 55 minutes to open the scoring courtesy of home debutant Tyler Goodrham.
Aaron Kuhl played a sublime ball over to Goodrham, whose exquisite touch sent him away to coolly slot the ball beyond Alan Julian, netting a goal on his home debut.
Soon after, Slough doubled the advantage with Matt Lench slamming home a cross at the back post after an inch perfect cross from Goodrham, who was increasingly causing problems with his direct running at defenders.
The third goal was coming and on 66 minutes, Slough buried the game.
Lench hooked a delightful ball across the field to Kuhl, who composed himself to strike the ball beyond the keeper into the bottom right of the net.
Lench, who was growing in confidence drove powerfully at the visitors’ defence and his strike deflected wide which led to the Rebels’ fourth goal.
A whipped corner from Lench on the right-hand side was met by Guy Hollis, who powered home an unstoppable header, celebrating in front of the jubilant supporters behind the goal.
Hampton & Richmond managed to find a consolation goal on 82.
After a melee in the Rebels box, Jorome Slew managed to pick the corner of the net through a crowd of bodies, but Slough will feel they ought to have cleared their lines before the strike at goal.
The game started frantically with the Rebels creating numerous opportunities to take the lead.
Within a minute of the kick-off Jonathan North’s long ball through the middle caused panic for the visitors’ defence; Alfonso Tenconi laid the ball back to Goodrham who had his goal-bound shot blocked.
Boro’ stopper Julian was called into action soon after, denying Lee Togwell a superb headed goal after meeting a Guy Hollis long throw down the left.
Tenconi was also denied an early goal, running behind the visitors’ backline but was unable to divert the ball beyond the onrushing Julian, who made a smart save.
With Slough dominating the opening exchanges, Freddie Grant whipped in a delightful deep cross from the left, Lench met the ball at the back post but blazed his effort over the bar.
Half time arrived with the game goalless, but an all-action second half saw the Rebels to all three points.
Hampton & Richmond Boro' Line up
Alan Julian, Ruaridh Donaldson, Dean Inman, Charlie Wassmer, Sam Deadfield, Jorome Slew, Jake Gray, David Fisher, Tyrell Miller-Rodney, Zach Dronfield, Imran Uche. Substitutes: Ryan Gondoh, Cole Brown, Niko Muir, Charles Hagan, Brandon Barzey.