Crawley welcomed back captain Dion Conroy to their starting line-up for the first time this season, but the 29-year-old defender was largely untroubled in a forgettable first half after kick-off had been delayed due to a medical emergency in the crowd.
The visitors improved after the break, with efforts from Paik Seung-Ho and Willum Willumsson dealt with by the Reds backline and goalkeeper Jojo Wollacott, while the hosts did not register a shot until the 71st minute.
They found themselves behind eight minutes later as Stansfield found space in the box to head in his 14th goal of the season shortly after Conroy was substituted.
Ethan Laird's brilliant solo run down the left and ball across the face of goal should have then been converted by Lyndon Dykes.
But the former QPR striker could not connect on the goalline to score his first league goal since moving to St Andrew's in the summer.