Alexander opened the scoring for the Rebels in the 7th minute, after the ball came out to Gabe George who saw his effort get blocked. Josh Jackman and Matt Lench then also saw their shots blocked before the ball fell to Alexander, who turned and drilled a low effort past Jack Turner, making it successive league games in which Alexander has scored at Arbour Park.
Francis Amartey nearly doubled Sloughs lead five minutes later, as the forward cut from on the left-hand side and struck an effort towards the bottom corner which was saved by Turner.
Slough were awarded a penalty kick in the 21st minute, after Alexander got past the Farnborough defence and had an effort saved by Turner, the ball came out to Amartey whose effort struck the hand of Adam Lovatt with the referee pointing to the spot.
Johnny Goddard stepped up and smashed the penalty straight down the middle to double the Rebels’ lead.
Goddard had a chance to get his brace in the 38th minute, as brilliant work down the right-hand side by Josh Jackman got him away from his man before setting up Goddard. The attacker’s low effort was comfortably saved by Turner, however.
Just before half time Goddard had another chance, after getting in behind the Farnborough defence with Turner rushing out and smothering the ball just in time.
Jackman nearly got the Rebels off to the perfect start to the second half in the 47th minute, after a corner from Matt Lench found the captain at the far post, but his effort went just wide of the post.
The visitors looked for a way back into the match and nearly got a goal back in the 56th minute after a corner found Freddie Grant on the near post, but the former Slough man’s header sailed just over Will Dennis’s crossbar.
In the 73rd minute, Lee Togwell lined up a strike from 25 yards which had to be superbly tipped away by Turner to deny the midfielder a goal.
Substitute Ogo Obi nearly got a third for the Rebels in the 81st minute after the forward closed down Turner, but the goalkeeper’s kick ricocheted off the Slough forward and just wide of the goal.
The Rebels held off late waves of Farnborough pressure for a huge three points, getting revenge for the 4-1 defeat at the visitors’ ground last month.
Slough turn their attention to next Saturday where they will face Weymouth on the road.
Jack Turner, Jack Ball, Freddie Grant, Ollie Robinson (Ricky Holmes 39), Kevin Lokko, Jon Page, Selim Saied, Mason Bloomfield, Tommy Willard, Jordan Norville-Williams (Alfie Saunders 27), Adam Lovatt (Courtney Fearn 46). Unused substitute: Rowan Silva.