Warren Harris opened the scoring with 13 minutes played, and Dyer scored his first from a similar position twelve minutes later to give Slough a 2-0 half time lead.
Dyer added a second on the hour mark and Darren Wheeler added a fourth fifteen minutes from time as Slough recorded a second consecutive 4-0 win.
This was a comfortable win against a previously unbeaten Barton side, who were without their top scorer Nathaniel Peacock. Darren Wheeler hit the top of the crossbar from 20 yards in the opening minutes, and Dyer saw a goal bound header blocked in the six yard box.
Dave Woozley could have given Slough the lead had he not miskicked in front of goal, but the Rebels were soon in front when Smith slipped a pass through to Harris, who fired past Beckwith from a narrow angle.
Jake Somerville needed to be alert to push a deep cross wide, and from the resulting corner, defender Andrews headed wide under pressure.
Slough doubled their lead on 25 minutes with Dyer’s first Rebels goal. Beckwith launched a long ball downfield, which was volleyed back into the Barton half by Ollie Burgess. Smith was standing in an offside position, but let Dyer run onto it and fire past Beckwith into the far corner.
Ryan Lake landed awkwardly and injured his knee shortly after, to be replaced by Wes Harrison – although Harrison would also pick up a knock in the second half and not see the game out.
Shortly before half time, Dyer headed onto the roof of the net from a well worked Wheeler corner as Slough ended the half strongly.
Barton started better in the second period, with Somerville called into action to claim a dangerous cross and a header from Bilal Hassan.
But at the other end Slough looked like scoring every time they poured forward. Smith lobbed a shot over the bar before a well worked move saw the ball played out wide on the right to Burgess, who delivered a low cross into the middle where Dyer got in front of his marker to nudge the ball past Beckwith and into the goal.
Smith went close twice more, the second a flicked header which Beckwith had to turn around the post.
On 75 minutes, shortly after Barton had made a substitution, a fourth goal arrived for Slough after good build-up play involving Dyer on the edge of the box. He turned and played in Wheeler, who ran onto the pass and drilled low into the far corner past Beckwith.
Recent signing Rob Carrick replaced the injured Harrison and Barton almost snatched a consolation goal when Woozley conceded possession, but Somerville made a good low save from Hassan.
Late on, Somerville made a fine save from substitute Paul Barnes, turning his fierce drive onto his own crossbar and away to safety, but Barton could not register a goal and Slough had their first home win of the season.
Barton Rovers Line up
Grant Beckwith, Peter Gatti, Ash Grinham, Tommy Hull (c), Paul Andrews, Liam McDevitt, Ricky Case, Alex O'Brien, Bilal Hassan, Bobby Dance, Rhys Hoenes. Subs: Jermaine Hall, Niran Vaughan, Paul Barnes, James Edgerley, Ryan Smales.