Pratley netted after 12 minutes but the Swans once again suffered a serious injury when Marcos Painter was carried off at the start of the second half.
The Swans had Artur Krysiak in goal for the injured Dorus de Vries with the 19-year-old Polish keeper making his League debut. Tom Butler replaced Mark Gower out wide for the only other change in the starting line-up.
The Saints, who had been beaten in their last three League games, almost found themselves a goal down in the second minute, but an offside flag prevented Jason Scotland from putting the Swans ahead.
A cross-field pass by Ferrie Bodde in the 12th minute to Butler did bring about the opening goal. Butler crossed hard and low to Pratley, who rifled a shot into the net.
The Swans should have doubled their lead five minutes before the break when Angel Rangel found himself clear on goal with only Kelvin Davis to beat, but his hurried shot hit the side-netting.
It took only 23 seconds of the second half for the Swans to attack the visitors' goal but Bodde's effort drifted wide.
In the 42nd minute, Painter became the second Swan to be stretchered off the field in successive matches after colliding with Saints full-back Lloyd James. Once again Alan Tate took the field as a substitute.
Swansea increased their lead in the 58th minute when Bodde's free-kick was pushed away by Davis, only for Gomez to tuck the loose ball home.
Butler made it three in the 72nd minute with his first goal of the season. He cut in from the left, easily evading a challenge from James and fired across Davis and into the far corner.
The Saints marginally improved on their dire first-half performance after the break but the Swans fully deserved their biggest win of the season.