Two goals from Crewe striker Lauri Dalla Valle in the space of three second half minutes condemned Crawley to back-to-back defeats for the first time in League One.
Dalla Valle turned an even contest in Crewe's favour when he headed home in the 62nd minute before making it 2-0 soon after.
Reds had chances of their own but were unable to take them as their poor run continued at Gresty Road.
Richie Barker's men have now taken only three points from their last six game but remain ninth in the table.
Reds went into the game aiming to maintain their impressive record of not losing two league games in a row under Barker.
They named an unchanged side to the one which went down 1-0 at home to Yeovil on Tuesday, with loan signing Conor Clifford on the bench.
Joe Walsh was also among the substitutes after suspension but Claude Davis was not available after the birth of his child.
The match was very open in the first half and it was surprising that it remained goalless at the interval.
Reds could have opened the scoring within 80 seconds when a cross from Nicky Adams found Gary Alexander at the far post whose shot came off the outside of the upright.
Crewe went straight down the other end with Dalla Valle diverting a low cross from Chuks Aneke inches wide.
Valle fluffed a good chance from a Bryon Moore cross after seven minutes and when the ball was put back into the centre Moore's low drive was kicked away by Paul Jones.
Adams was proving a constant threat down the right and whipped over a series of crosses which the Crewe defence and goalkeeper Alan Martin struggled to deal with.
The Reds winger had switched to the left when he swung over a ball which Mark Connolly headed down and over the bar at the far post.
Reds suffered a blow just before half-time when Kyle McFadzean, who is still suffering from a virus, had to go off and was replaced by Joe Walsh.
Crewe came out quickly after the restart and should have taken the lead within two minutes. Paul Jones could only push out a header from Mark Ellis but Luke Murphy somehow hit the bar with a follow up shot.
Reds wasted a glorious chance of their own in the 57th minute when a free kick from Billy Clarke was flicked on by Mark Connolly to Gary Alexander but his shot was saved at point blank range by Martin.
It proved pivotal as Crewe took the lead five minutes later. Murphy swung over a free kick and ]Dalla Valle's glancing header looped over Jones and inside the far post.
Dalla Valle grabbed his second three minutes later when Moore got the wrong side of the Reds defence and although he mishit his shot the ball rolled kindly to Dalla Valle to stab home from close range.
Reds boss Richie Barker responded immediately by bringing on Nicky Ajose and switching from 4-4-2 to 4-3-3 and the on-loan Peterborough striker focred Martin into a low save with 15 minutes to go.
Clifford also came on for his debut with six minutes remaining but could not help Crawley get back into the game and it was Crewe who almost extended their lead when Matthias Pogba chipped just wide.