The Rebels put on a strong first-half performance with the wind at their backs and Matthew Lench gave them the lead, but Slough were pegged back on the stroke of half-time courtesy of a fine strike from Moses Emmanuel.
And Manny Williams struck the winning goal from the penalty spot on 70 minutes as Slough continued their unbeaten run in March.
The early chances fell to the Rebels, Lench seeing an early effort deflected wide, and just minutes later Williams had an effort blocked in the goalmouth as Slough looked to take advantage of the windy conditions.
Billericay had their first clear sight of goal in the 17th minute as Jake Robinson attempted to dink the ball over Jack Turner when one-on-one, however the Slough shot-stopper stood tall to keep the scores level.
Guy Hollis’ long throws would continually cause confusion amongst the Billericay defence. In the first instance the ball fell to Mark Nisbet in the box, but he could not get his shot away.
Francis Amartey had his first effort blocked after a storming run from the left channel into the box in the 26th minute, as the young striker looked to add to his effort at Concord Rangers last weekend.
But Slough would break the deadlock in the 32nd minute through Lench. Following another Hollis throw in, Lench made space in a crowded penalty box for a smart finish low past Alan Julian to put The Rebels ahead.
That lead should have been doubled moments later after Warren Harris’ effort from outside the box crashed against the post. The ball then fell nicely for Williams, who could not direct his effort into the empty net.
And the visitors equalised just moments before the break. A whipped delivery into the box found Emmanuel at the back post, and he emphatically volleyed his side level.
The second-half began with Robinson firing in a fierce free-kick from just outside the box, but Turner got a strong hand to the ball and turned it away.
Neither side created anything further of note until Slough won a penalty on 68 minutes.
Billericay were penalised as Ross Lafayette appeared to handle a strike at goal, with referee Richard Gardner well placed to point to the spot. Williams took the penalty after a delay, and finished calmly into the bottom corner to put The Rebels in the driving seat.
Just minutes later Slough found themselves through on goal once again. The gusty wind played into the favour of Harris, who saw the ball drop perfectly into his stride. His powerful run forced Billericay into last-ditch defending which denied the winger a shooting opportunity.
Moments later, tempers flared as an altercation saw Billericay lose star striker Jake Robinson to a red card after Lee Togwell had won a free kick.
The dismissal did not stop Billericay from piling on pressure in the closing stages, and just four minutes later the goal-scorer Emmanuel would go close with a powerful effort, but Turner was equal to it.
Alan Julian made an important save from a Lench free kick and Amartey, who looked bright all game, would go close to scoring a deserved goal. Taking Lee Togwell's pass and forcing his way up the pitch, the striker’s left-footed effort looked destined for the back of the net, however another stunning save from Julian denied him.
The Rebels were able to see out the remainder of the game and gain a deserved three points, and can now look forward to a trip to promotion hopefuls Woking, who drew 3-3 with Welling this weekend.
Report: Sam Collard
Billericay Town Line up
Alan Julian, Joe Kizzi, Michee Efete, Cole Kpakawa, Lloyd Doyley, Jake Howells (c), Moses Emmanuel, Danny Waldren, Jake Robinson, Ross Lafayette, Jamar Loza. Substitutes: Alfie Potter, Jamie O’Hara, Paul Rooney, Tambeson Eyong, Kieron Cadogan.