Swailes, who had just forced Mansfield keeper Kevin Pressman into his first save - a brilliant reflex close-range stop - levelled from the resulting 78th minute corner.
Mansfield failed to clear Paul Harsley's flag kick and Swailes finally bundled the ball over the line after a melee in the six-yard area.
In a thrilling finish Macclesfield keeper Alan Fettis denied Mansfield a late winner, diving full length to kick away Kyle Jacob's stinging 30-yard drive.
Mansfield fans, who had staged a rally and march against chairman Keith Haslam before the kick-off, held up red cards at the crunch game's first corner in a further protest.
When midfielder Giles Coke was fouled from the corner Adam Rundle's 20-yard drive from the follow up grazed the bar.
In a scrappy start dominated by Mansfield that was the only chance until the half-hour when Fettis did well to hold on to Gus Uhlenbeek's 20-yard pile-driver.
Fettis did even better three minutes before half-time to collect Danny Reet's close-range shot after a neat turn.
Inside the first 30 seconds of the second half the keeper repeated his heroics to parry long-range efforts from Gareth Jelleyman and Adam Rundle, while Swailes blocked Coke's follow-up.
Rundle was again thwarted by the diving Fettis five minutes later, and when the keeper was beaten, the wing-man's diving header from an excellent Jacobs cross flew narrowly wide.
But Rundle could not be denied and in the 57th minute gave Mansfield the lead. Harsley failed to cut out Jacob's excellent cross-field pass and the wing man pounced to lash the loose ball into the roof of the net from 12 yards.