The Stags made life difficult for themselves on Tuesday evening at Field Mill when Tony Vaughan was sent off after 18 minutes for violent conduct.
The visitors then took the lead through Andy Robinson on 31 minutes, as the South Wales club were 1-0 up at the break.
However, Keith Curle's side would draw level when Liam Lawrence (pictured) scored from the penalty spot to earn Mansfield a point while Swansea are five points adrift of the play-off places.
Carlisle United kept their hopes of an improbable escape from the foot of the Division Three table alive with a 3-2 away win at Scunthorpe United.
The Cumbrians took the lead three times at Glanford Park - with the first coming after a quarter of an hour through Peter Duffield.
On-loan Iron striker Steven MacLean equalised on 28 minutes for Scunthorpe, as both sides went into the break at 1-1.
Recent signing Mark Boyd restored Carlisle's lead ten minutes after half time before MacLean made it 2-2 with a penalty on 73 minutes.
However, Paul Simpson's side would take more crucial points towards their Football League survival hopes when Chris Billy made it 3-2 four minutes later.
The result keeps Carlisle seven points adrift of safety in the Third Division table.
Click below for match summaries:
Division Three
Mansfied 1-1 Swansea
Scunthorpe 2-3 Carlisle
Click here for an updated Division Three table.
