Crawley started well kicking down the slope with Henry Mungwira and Aaron Browne both having early shots blocked.
Rangers responded with an effort from Vinny Greco which was blocked by Crawley new boy Mario Santos-Costa.
Mungwira then set up JJ Billy but his shot was saved by Jack Brooker in the Rangers goal. Minutes later Aaron Browne fired a free kick straight at Brooker.
Sam Peverall, Stuart Strange and Mungwira all had efforts while just before half time Billy fired over from close range.
Jones left frustrated once more as Town fail to take their chances during Lilywhites defeat
Goal-shy Luton still searching for a first win after Preston defeat
Jones assures Lockyer and co they are still 'key' members of Luton's squad
Hatters were aware of McAtee's shoulder injury before agreeing to sign Grimsby striker
'Embarrassed' Hatter boss hits out at one of the 'worst' individual performances he has ever seen after Town's cup exit to Exiles
Crawley finally took the lead four minutes into the second half when Peverall whipped in a corner and it was turned in by Tom Barnett at the near post.
Rangers responded well and pushed forward. Sam Ward and Greco both had shots saved by Dean Bull before Danny Gray shot wide from close range.
Back came Crawley and Browne came close to doubling the home side’s lead but his lob over Brooker went just over the bar.
In the 83rd minute Crawley doubled their lead. Strange received a throw in on the right and knocked in a peach of a cross. Mungwira rose to head over the outstretched arm of Brooker.
Rangers refused to lie down and in the sixth minute of added time pulled one back with a goal from Sam Ward.