The Tykes pulled one back through Darren Moore but Swansea dominated for long periods and fully deserved the victory
After only four minutes, the Swans should have taken the lead following a mix-up in the Barnsley defence.
The unmarked Kuqi went into the penalty area with the ball at his feet but, with an empty goal in front of him, he somehow managed somehow to screw his shot wide. It was an incredible miss as Kuqi had enough time to have walked the ball into the net.
The Swans looked a bit nervous in the opening stages but Pratley and David Cotterill began seeing more of the ball and most of the play was around the visitors' goal.
They went ahead in the 23rd minute when the Tykes failed to clear a corner, the ball bobbed about in the six-yard box, and Williams swooped in to lash home.
Five minutes later Kuqi made amends for his earlier miss by diving low to head home a cross from Mark Gower to double their lead.
But theTykes hit back out of the blue in the 35th minute when centre-half Moore rose above Dorus de Vries to head in a corner from Iain Hume for his first goal of the season.
Cotterill headed a Cedric van der Gun cross high over the bar and a Kuqi flick was saved at the second attempt by Barnsley goalkeeper Luke Steele as the first half drew to a close.
Van der Gun was lively down the flank and he forced Steele to push behind on the hour as the Swans pressed for the goal to give them breathing space.
A fine run from Andrea Orlandi led to the Swans deservedly increasing their lead in the 72nd minute. The midfielder, who had replaced Gower two minutes earlier, sped down the left before crossing to Pratley who fired high into the net from just inside the area.
All three substitutes were used by Swansea but they were unable to add to their score despite pinning Barnsley back on defence for the final minutes.