The Swans took the lead with only five minutes on the clock when Pratley beat the offside trap to slot home and he doubled his tally before the break when his powerful finish ended a fine move.
Wednesday, without a goal in the last six, barely looked like registering, with Darren Purse's header their best effort.
The Owls are now winless in the last 10 having lost the last six and face the harsh reality of relegation if they do not make drastic improvements, while Swansea pick up their fourth away win of the campaign and stay in play-off contention.
Wednesday could not have made a worse start as they fell behind to the first meaningful attack of the game in the fifth minute.
Gorka Pintado picked the ball up on the left and flighted a fine pass over the top and, with Wednesday trying to play the offside trap, Pratley ran clear before slotting the ball past Lee Grant.
The hosts responded positively, though, and nearly levelled twice in a minute.
First Jermaine Johnson's 25-yard drive was palmed over by Dorus De Vries and, from the resulting corner, Purse's header was beaten away by the Dutch keeper.
Wednesday were not able to capitalise, though, and they soon lost any momentum.
Johnson was a continued threat on the wing but wasted possession, while the hosts were always vulnerable to the Swansea counter-attack.
And so it proved 10 minutes before the interval as Pratley got his and Swansea's second with a wonderfully-crafted goal.
There was an interchange of passes before Andrea Orlandi set the dangerous Nathan Dyer free and he beat his full-back before centring for Pratley, who met the cross with a low and powerful shot from 12 yards out to bag his fourth of the campaign.
McAuley's men did improve after the break and controlled the majority of the possession but their lack of creativity in the final third told and De Vries had very little to do.
Substitute Francis Jeffers did have a golden opportunity to get one back when he found himself in space in the penalty area but a heroic piece of defending by skipper Alan Tate saw Jeffers' shot blocked.
Swansea offered very little as an attacking force in the second period and they seemed content to sit on their lead.
However, as much as Wednesday huffed and puffed they were not able to make the breakthrough and were subjected to a chorus of boos at the full-time whistle.