Joe O’Neill’s second half goal at Little Wembley on Saturday was enough to fire Nelson up to eighth place.
Mike Fletcher made way for Sam Howell in Mark Fell’s only change, and Howell and Ben Hoskin both had firm shots charged down early on.
Ed O’Neill twice sent efforts wide, before Kieran Walmsley had a shot from distance saved by Dale Eve.
Scott McGowan went clear for Congleton, but Ben Woodhead palmed his effort wide, before a sliced clearance from a Blues defender rebounded off the bar to safety.
Joe O’Neill headed over from an Alex Porter corner as the sides went in level.
On the hour, Matt O’Neill created an opening for brother Joe, who advanced and beat Eve.
That proved to be the winner, although substitutes Jonny Hession and Paul Fildes combined late on, with the latter unable to beat Eve with a header.