A goal from Ryan Williams and a brace from Tim Sills gave Aldershot their first win of the season and lifted then off the foot of the table.
Crawley's misery was added to after they had James Donavon sent off for picking up two cautions.
Aldershot enjoyed the best of the early possession and could have taken the lead as early as the seventh minute but Chris McPhee blasted wide from only six yards.
Surprisingly, it was Crawley who took the lead on eight minutes when Daryl Clare volleyed in Stuart Douglas' knock down after Sacha Opinel had played the ball into the box.
The goal seemed to kick Aldershot into life and Williams levelled the scores in the 29th minute with a spectacular effort. The midfielder punished Donovan's foul on Sills by blasting home a free-kick from 20 yards that burst into the top-left hand corner of the net.
Shortly before half-time, Sills added Aldershot's second when he headed home McPhee's cross from the left-flank. The powerful centre forward rose highest in the box to steer the ball in from six yards.
Crawley were then reduced to 10 men when Donovan received his marching orders after bringing down Sills in the penalty area.
Referee Mr Desmond had already booked the defender for unsporting behaviour in the 17th minute and did not hesitate to send him for an early bath.
Sills stepped up and converted the resulting spot-kick, sliding his right-foot shot into the bottom right hand corner in 68th minute.
Crawley were given some consolation when Simon Wormull reduced the deficit in the 83rd minute. The midfielder struck a sweet drive from 20 yards to bring the match to a climax for the remaining minutes.
But, Aldershot managed to cling on to their one-goal advantage and take all three points.