The home side took a 2-0 lead in a thrilling first half and sealed the win late on with a Jordan Rhodes goal.
Aldershot started brightly and put Brentford to the sword early on but the home side gradually took control and were full value for the win in the end.
The first goal had a controversial element to it as Referee Pat Miller looked set to disallow Marcus Bean's strike for offside.
The midfield man lashed home from eight yards as the ball had came to him off Aldershot's Scott Davies. Mr Miller awarded the goal after consultation with his assistant.
Brentford should have doubled their lead ten minutes later when a penalty was awarded for a foul by Chris Blackburn on Charlie MacDonald.
Blackburn escaped a red card for the last man foul and MacDonald saw his penalty saved by Aldershot goalkeeper Mikhael Jaimez-Ruiz.
MacDonald smashed a shot against the bar seconds later but made no mistake with his second penalty attempt just before half time.
This one was awarded when Anthony Charles deliberately hand-balled Rhodes' goal-bound shot, the defender again escaped with a yellow card but this time MacDonald beat Jaimez-Ruiz from the spot.
Bean hit the outside of the post with a header for the home side and Rhodes shot wide when he raced clear with only Jaimez-Ruiz to beat as well as pulling a shot wide from the edge of the box.
Brentford goalkeeper Ben Hamer made a some vital saves either side of half time, firstly from Kirk Hudson and then from John Grant before Louis Soares shot wide after racing clear.
Jaimez-Ruiz saved well from MacDonald and Adam Newton but could do nothing to prevent Rhodes notching a goal on his home debut.
The on-loan striker picked up a MacDonald lay-off and slipped past two Aldershot defenders and coolly slotted the ball home with three minutes remaining.