Crawley have had a four-point deduction for fielding an unregistered player reduced to one point after a successful appeal to the Football Association.
Club representatives, including a barrister, met with the FA appeal board for four hours to discuss the appeal.
Crawley chairman Vic Marley told the club website: "We are all delighted that justice has prevailed."
In a statement, the Football Conference said it had "no issue" with the final decision from the three-man commission.
The Red Devils' appeal, heard at FA headquarters in Soho Square, was headed by barrister Adam Lewis and attended by Marley, as well as directors Susan Carter, Steve Mansell and Barry Munn.
Marley said: "We were given a full and fair hearing.
Our supporters, players and staff are the most important people in all of this
Crawley chairman Vic Marley
"At this stage I must thank our barrister for presenting our case, which we knew from the outset was strong.
"I will now take time to reflect on this decision, speak with my fellow board members, take advice once again from Adam and then issue a full statement in due course.
"That will in turn educate our supporters, players and staff who after all are the most important people in all of this."
The decision sees Oxford, who were also deducted points, overtake Crawley into seventh place in the Blue Square Premier.
The Football Conference have confirmed they hope to reveal their findings on an internal review into their registration system, after a season which has also seen two other Blue Square Premier teams Mansfield and Oxford, as well as Blue Square South side Bognor Regis Town, deducted points.
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