The midfielder tucked home from 12 yards after goalkeeper Ross Fitzsimons was sent off for lashing out at Jimmy Smith inside the area having claimed a corner.
Payne’s composed spot-kick was enough to seal the points for the visitors, who had taken a first-half lead through Smith.
Jon Stead equalised from the spot in the second half when Josh Lelan was adjudged to have handled inside the area.
County poured forward in search of a winner and created heavy spells of pressure but they could not find a way through a stubborn Crawley defence.
And their cause was not helped when on-loan Liverpool midfielder Matty Virtue was sent off for a second bookable offence in the 90th minute.
Morecambe have no fresh injury concerns ahead of Tuesday's Sky Bet League Two home clash with Colchester.