Goals in each half by former Shots striker Omari Coleman and Michael Bostwick sealed the points for the relegation battlers.
Aldershot were poor throughout but could have taken the lead after seven minutes.
Matt Somner opted to cross instead of shooting after been left unmarked at a free-kick six yards out and the chance was cleared.
Danny Ekoku should have scored for the home side on 26 minutes when he fired a low shot straight at keeper Nikki Bull, but the Crawley fans only had to wait another two minutes before Coleman broke the deadlock.
Bull spilt a 20-yard drive by Lee Blackburn and Coleman was quickest to react as he slid the ball home.
The Reds made the game safe with the killer second goal on 55 minutes.
Teenager Bostwick, who was making his first league start, slammed into the bottom corner from the edge of the box after a neat lay-off by Ekoku.
Kirk Hudson spurned a golden chance to pull one back for the visitors 20 minutes from time when he had a shot saved at point-blank range by Phil Smith after been sent clean through on goal.