Three goals in 11 minutes from Ashley Harris, Luke Rodgers and Izale McLeod sealed victory for Appleton's men in Sunday's League One encounter at the Broadfield Stadium, after Crawley had Josh Simpson and Hope Akpan sent off.
Appleton said: "You have to admire the work ethic our players have showed and this result has been coming for a while.
"I always thought it would be our day. I am glad we kept our discipline because it is easy for the referee to level things up after two sending-offs.
"It's pleasing to get a result like this for the fans because they give us tremendous support home and away every week. This is for them."