Strikers Dave Stevens and Danny Hockton scored the goals that got Crawley's push for promotion from the premier division back on track at the Moorlands on Saturday.
Reds boss Billy Smith went to Moor Green looking for three points following his side's recent run in the FA Cup.
Smith said: "I was very pleased. It was a hard game for sure and Moor Green were a decent side so to come away with three points is very satisfying.
"Andy Little was excellent in goal for us and really kept us in the game at times, and I thought Peter Fear gave a fine captain's performance."
Smith introduced new signing Barry Moore in place of the injured Ben Judge, while Ian Payne continued for the suspended Ernie Cooksey.
After just five minutes, a deep cross from the tricky Mo Harkin saw Neil Le Bihan just fail to connect at the far post.
Moor Green then took the initiative and, after nutmegging Marc Pullan, striker Nathan Lamey was denied by Little.
It was not to be the last time, as Lamey endured a frustrating afternoon at the hands of the Crawley keeper.
Little went on to deny Lamey again on 24 minutes before saving with his legs from Danny Scheppel, while Harkin was denied by a goal-line clearance at the other end.
On 34 minutes, Reds took the lead as Harkin put Stevens through and he fired in despite keeper Adam Rachel getting a hand to the ball.
Little made a point blank stop to keep out Lamey, while at the other end Hockton was denied on the line after the break.
It was Hockton who settled the victory two minutes from time as he glanced in Fear's free kick past Rachel, handing Crawley three points which were richly deserved for their tireless work.
Moor Green: Rachel, Hughes, Petty, Gillard, Sanders, Scheppel, Stanley, Laney, Gayle, Evans, Myers. Subs: Blake, Fitzpatrick, Walker, Saulds, Robinson.
Crawley: Little, Moore, Payne, Hooper, Pullan, Fear, Holmes, Harkin, Hockton, Stevens, Le Bihan. Subs: Bagnall, McDonnell, Brake, Hemsley, McKoy.
Referee: Mr I. Batchelor (Bicestor).
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