A man on match performance by Swansea keeper Roger Freestone and a fatal error by his opposite number handed the Swans a vital three points.
Macclesfield Town manager David Moss branded Steve Wilson's a schoolboy error when he gifted Matt Murphy the winning goal after 83 minutes.
Wilson was robbed on the byline by Michael Howard and left Murphy the grateful recipient of the resulting cross, but the late score would have been meaningless had Freestone not been in great form.
The 34-year-old had received a painkilling injection two days before the game, but showed no signs of vulnerability as he denied Matthew Tipton, Danny Whitaker and Chris Priest.
Freestone's save from Whitaker just minutes before the break was magical and ensured the Swans stayed in the game at half time.
Swansea hadn't really come close to troubling Wilson at the other end, but Jamie Wood's introduction after the interval gave the basement club a fresh start.
The terrier-like Paul Reid soon tried his luck with a long-range effort as did sub Andrew Mumford but it was the Silkmen who came closest to opening the scoring, with the home defence not standing as firm as Freestone did behind them.
Tipton was given an open invitation to shoot by the Swans back four, who had Freestone to thank again as he palmed the ball away.
Only James Thomas' tireless running looked like giving the Swans the lead, but it was strike partner Murphy who anticipated Wilson's mistake from Howard's cross.
Visiting manager Moss had no doubts who won the game for the home side: "Roger has been a cracking keeper for a number of years now and kept them in the game by pulling off some great saves."