Villa slumped a massive 12 points short of safety with another poor display as the Swans put daylight between themselves and the drop zone.
On a dull night at the Liberty Stadium, Guzan came off his line to punch clear a free-kick ten minutes into the second half.
But the stopper completely missed it and the ball cannoned off his shoulder, hit Swansea defender Federico Fernandez and looped into the Villa net.
It remained 1-0 and handed Remi Garde a sixth straight Premier League defeat.
MORE TO FOLLOW