And it needed Andy Robinson to once again keep their promotion hopes alive after he scored one and set up another to mark Roberto Martinez's first home win.
Robinson smashed home a 76th minute spot-kick after Pawel Abbot was fouled in the box to make it two in two weeks after his strike at Tranmere last week.
Then the midfielder continued his impressive form by swinging in a corner to let Izzy Iriekpen head home the second and move the Welshmen into the play-off places.
But it only came after the hosts laboured against the relegation threatened Spireites.
Swansea had failed to make the most of their early chances but were denied a 26th minute opener when Phil Picken made an excellent last-gasp tackle to stop Robinson.
As Swansea's push continued, Chesterfield keeper Barry Roche had to save well to keep out Tom Butler moments later.
Then Dennis Lawrence saw his shot bounce off the top of the bar as the hosts pushed without any reward.
But Chesterfield managed to contain Martinez's men and frustrate the fans, enjoying one good chance of their own as tension grew.
Keeper Willy Gueret spilled Alex Bailey's speculative effort but substitute Paul Shaw somehow managed to fire over from close range.
But Swansea struck when Reuben Hazell hauled down Abbott inside the area and Robinson made no mistake from the spot.
Then the midfielder's corner allowed Iriekpen to glance home the second to seal the points and move Martinez's side into the top six.