Fleetwood registered their first home win as a Football League club in a game which ended as 10-a-side.
Junior Brown found the corner to put them ahead but team-mate Dean Howell was sent off for handling on the line.
Keeper Scott Davies saved Josh Payne's penalty, only for Craig Reid to bring Aldershot level via the crossbar.
Steve McNulty headed Fleetwood back in front and Brown and Andy Mangan also found the net after Payne's handball earned him a second yellow card.
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Aldershot Town manager Dean Holdsworth told BBC Surrey:
"If you were here it was not a one sided game and they took advantage at the end when we were stretched. But there were some key moments in this game that we've not taken advantage of.
"We've given a cheap free-kick away and then a free header in the box and you can't do that at this level and I'm disappointed in that.
"Everything we've done preparation wise has been as professional as we can and when players go over the line you've got to trust them.
"If you start losing trust in players then you'll find themselves out of the team."