In-form Shay McCartan extended Stanley’s unbeaten run to 15 games as they boosted their bid for a play-off place.
The Reds, with a cluster of other teams, moved to within two points of the play-off places thanks to McCartan’s 11th goal of the season on 48 minutes.
Crawley started well with their 20-goal hitman James Collins firing a shot just wide in the third minute after a clearance rebounded off the Stanley defence into his path.
Chances were at a premium in the opening 20 minutes with neither keeper tested.
Billy Kee had Stanley’s first shot on target in the 20th minute from the edge of the area but it was easy for keeper Glenn Morris while, a minute later, Matty Pearson was denied by the stopper at the near post.
Stanley began to find their feet with a 35-yard Shay McCartan free kick collected low by Morris.
However Crawley were still a threat and, on 28 minutes, it took a superb sliding block by Mark Hughes to deny Collins a clear-cut shooting opportunity.
Stanley came close on 32 minutes when McCartan’s shot was deflected to Pearson six yards out and his goalbound effort blocked.
That was it for the first half with Crawley looking strong and Stanley struggling to impose themselves on the game.
Stanley started the second half with urgency and scored the opener on 48 minutes when Sean McConville played a great ball for McCartan to race free. He was tackled by keeper Morris but dinked the ball into the net for his 11th goal of the season.
The Reds looked dangerous and then enjoyed a period of pressure but Crawley were always a threat.
Omar Beckles could have made it safe for Stanley on 76 minutes with a free header from a McConville ball in but it was straight into the arms of Morris.
Crawley almost equalised on 81 minutes when a curling shot from Josh Payne could only be palmed out by Marek Rodak but Collins blasted the follow-up over the bar.
Stanley had to withstand late pressure but held on to preserve their unbeaten home record in 2017 and a crucial three points.