After just 68 seconds the Shots took the lead when Brett Johnson firmly headed past Mark Osborn.
Minutes later Johnson was involved in the action again, forcing a good reaction save from Osborn.
The Shots remained on top as they piled on the pressure. However, in the 17th minute Farnborough were handed a lifeline when Johnson's shove on Robert Traynor led to the referee immediately pointing to the spot.
Former Aldershot striker Chukki Eribenne stepped up only to hit the post as keeper Nikki Bull dived the opposite way.
Eribenne and David Lee were off target for their respective sides before the Shots were awarded a penalty of their own.
Osborn brought down Jake Robinson the but Lee, who had scored a penalty against Exeter on Tuesday, saw the Farnborough keeper save his effort and then block Nick Crittenden's shot from the rebound.
Aldershot made it 2-0 in the 54th minute when Crittenden scored with a great 20-yard strike from Tim Sills' cut-back.
Borough pulled one back when Tony Taggart turned in Robert Traynor's cross and Bull then saved well from Taggart before the Shots restored their two-goal cushion thanks to Robinson's 69th minute strike.