A 53rd minute headed goal by Jon-Paul Pittman decided the game from a Dannie Bulman free-kick.
Pittman was later sent-off for picking up his second yellow card and Reds had a battle on their hands as the Shots pressurised the Crawley penalty area.
However goalkeeper Ashley Bayes proved up to the task and manged to keep a clean sheet as Town completed their third victory of the season and first away from home.
Town made three changes to the side which beat Northwich Victoria 2-1 on Saturday. New signing James Krause made his debut at left-back in place of Jamie Lovegrove.
Guy Madjo returned up front in place of Pierre Jospeh-Dubois while Jamie Cook replaced Steve Evans in midfield.
Aldershot fielded an unchanged line-up which beat Histon 2-1 away on Friday night.
SHOTS: Bull, Straker, Day, Charles, Chalmers, Grant, Dixon, Davies, Hudson, Harding, Gier. Subs: Soares, Elvins, Hylton, Winfield, Jaimez Ruiz
CRAWLEY: Bayes, Bull, Krause, Stevens, Mills, Thompson, Bulman, Madjo, Vieira, Cook, Pittman. Subs: Joseph-Dubois, Ujah, Lovegrove, Evans, Clapham.
Ref: G.D.Scott
ATTENDANCE: 2,457
OBSERVER MAN OF THE MATCH: Ashley Bayes
Updates:
2 mins - John Grant had a superb strike from eight yards well-saved by Ashley Bayes
10 mins - Jamie Cook turned an opponent and played the ball through to Madjo, who tried to round keeper Nicki Bull but the Shots' custodian got his fingers to the ball and cut the chance out.
11 mins - Cook fired over the bar from the edge of the box after Dannie Bulman played the ball to him from a corner.
16 mins - A long throw-in by Shots' Lewis Chalmers found defender Anthony Charles from six yards out but his header flew inches over the crossbar.
21 mins - An inswinging corner by Aldershot's Scott Davies at the far post was met by Grant but rose just over the bar.
22 mins - Crawley's Madjo beat a player down the right flank and blasted the ball against Jon-Paul Pittman, who inadvertantly blocked the on-target shot.
38 mins - Vieira played the ball for Madjo on the left flank, whose cross was not controlled by Cook on the far post, and the ball flew over the top.
43 mins - Anthony Straker ran through into the penalty area, his strike was parried by Bayes. Former Crawley loan player Jonny Dixon followed up and looked like he was going to tap into an empty net, but the chance was well blocked by Jamie Stevens.
44 mins - A corner by Aldershot's Scott Davies, who is on loan from Reading, was met by the head of defender Charles and was heroically cleared off the goalline by Crawley's Ronnie Bull.
45 mins - Town finished with an attack of their own as Cook showed great skill to beat two players on the right, cut inside into the penalty area and produced a left-footed shot which was saved by the legs of Nikki Bull.
Half-time: Aldershot Town 0 Crawley Town 0
53 mins - GOAL (0-1) Crawley took the lead when a free-kick by Dannie Bulman was headed into the top of the net from long range by Jon Paul Pittman. He then received a yellow card for celebrating in front of Aldershot fans.
55 mins - Aldershot came close to scoring an equaliser when Davies' free-kick was tipped onto the post by Ashley Bayes.
56 mins - Dixon then had a go from short-range but was denied by a point-blank save by Bayes
58 mins - Jamie Stevens received treatment to his head on the pitch after a challenge but after a delay was able to continue playing.
67 mins - Reds were reduced to 10 men after Pittman was sent-off for receiving his second yellow card for a late challenge on Rob Gier.
72 mins - Aldershot bombard the Crawley goal when first substitute Louis Soares hit the post, John Grant had a shot from 25 yards to which Bayes performed a great save to turn round the post.
75 mins - Tyrone Thompson was booked for pulling a shirt.
76 mins - Aldershot's Rhys Day nodded against the crossbar from the six-yard box.
81 mins - Crawley made their fist substitution when Stephen Evans replaced Magno Vieira.
84 mins - Grant went wide with a shot from outsdie the area after being played through by Ben Harding.
88 mins - Town make a second substitution as striker Pierre Joseph Dubois came on for Madjo
Crawley held on for five minutes of added time.
Full-time score: Aldershot Town 0 Crawley Town 1
Pittman was later sent-off for picking up his second yellow card and Reds had a battle on their hands as the Shots pressurised the Crawley penalty area.
However goalkeeper Ashley Bayes proved up to the task and manged to keep a clean sheet as Town completed their third victory of the season and first away from home.
Town made three changes to the side which beat Northwich Victoria 2-1 on Saturday. New signing James Krause made his debut at left-back in place of Jamie Lovegrove.
Guy Madjo returned up front in place of Pierre Jospeh-Dubois while Jamie Cook replaced Steve Evans in midfield.
Aldershot fielded an unchanged line-up which beat Histon 2-1 away on Friday night.
SHOTS: Bull, Straker, Day, Charles, Chalmers, Grant, Dixon, Davies, Hudson, Harding, Gier. Subs: Soares, Elvins, Hylton, Winfield, Jaimez Ruiz
CRAWLEY: Bayes, Bull, Krause, Stevens, Mills, Thompson, Bulman, Madjo, Vieira, Cook, Pittman. Subs: Joseph-Dubois, Ujah, Lovegrove, Evans, Clapham.
Ref: G.D.Scott
ATTENDANCE: 2,457
OBSERVER MAN OF THE MATCH: Ashley Bayes
Updates:
2 mins - John Grant had a superb strike from eight yards well-saved by Ashley Bayes
10 mins - Jamie Cook turned an opponent and played the ball through to Madjo, who tried to round keeper Nicki Bull but the Shots' custodian got his fingers to the ball and cut the chance out.
11 mins - Cook fired over the bar from the edge of the box after Dannie Bulman played the ball to him from a corner.
16 mins - A long throw-in by Shots' Lewis Chalmers found defender Anthony Charles from six yards out but his header flew inches over the crossbar.
21 mins - An inswinging corner by Aldershot's Scott Davies at the far post was met by Grant but rose just over the bar.
22 mins - Crawley's Madjo beat a player down the right flank and blasted the ball against Jon-Paul Pittman, who inadvertantly blocked the on-target shot.
38 mins - Vieira played the ball for Madjo on the left flank, whose cross was not controlled by Cook on the far post, and the ball flew over the top.
43 mins - Anthony Straker ran through into the penalty area, his strike was parried by Bayes. Former Crawley loan player Jonny Dixon followed up and looked like he was going to tap into an empty net, but the chance was well blocked by Jamie Stevens.
44 mins - A corner by Aldershot's Scott Davies, who is on loan from Reading, was met by the head of defender Charles and was heroically cleared off the goalline by Crawley's Ronnie Bull.
45 mins - Town finished with an attack of their own as Cook showed great skill to beat two players on the right, cut inside into the penalty area and produced a left-footed shot which was saved by the legs of Nikki Bull.
Half-time: Aldershot Town 0 Crawley Town 0
53 mins - GOAL (0-1) Crawley took the lead when a free-kick by Dannie Bulman was headed into the top of the net from long range by Jon Paul Pittman. He then received a yellow card for celebrating in front of Aldershot fans.
55 mins - Aldershot came close to scoring an equaliser when Davies' free-kick was tipped onto the post by Ashley Bayes.
56 mins - Dixon then had a go from short-range but was denied by a point-blank save by Bayes
58 mins - Jamie Stevens received treatment to his head on the pitch after a challenge but after a delay was able to continue playing.
67 mins - Reds were reduced to 10 men after Pittman was sent-off for receiving his second yellow card for a late challenge on Rob Gier.
72 mins - Aldershot bombard the Crawley goal when first substitute Louis Soares hit the post, John Grant had a shot from 25 yards to which Bayes performed a great save to turn round the post.
75 mins - Tyrone Thompson was booked for pulling a shirt.
76 mins - Aldershot's Rhys Day nodded against the crossbar from the six-yard box.
81 mins - Crawley made their fist substitution when Stephen Evans replaced Magno Vieira.
84 mins - Grant went wide with a shot from outsdie the area after being played through by Ben Harding.
88 mins - Town make a second substitution as striker Pierre Joseph Dubois came on for Madjo
Crawley held on for five minutes of added time.
Full-time score: Aldershot Town 0 Crawley Town 1
Source: http://www.crawleyobserver.co.uk/ViewArticle.aspx?sectionid=497&articleid=3149564