An 88th-minute penalty from Ashley Carew took Dulwich into the second qualifying round of the FA Cup.
In a game of few clear opportunities, it was Dulwich who took advantage of their opportunity to progress after Rhys Murrell-Williamson was brought down in the box two minutes from time.
After the away side missed a number of good opportunities in the first half, the game looked to be heading for a replay until Murrell-Williamson accelerated towards goal and was fouled by Joe Hicks, who was scampering back to cover.
Carew kept his cool to convert from the spot and though Hampton pressed forward and hurled a couple of long throws into the box late on, they were unable to force an equaliser.
Dulwich will now play East Sussex side Whitehawk in the next round on September 26.