The midfielder, who is keen on a switch to interested Nottingham Forest according to Reds chief executive Mark Arthur, grabbed the killer second goal for the Swans at the Liberty Stadium before taking off his shirt and celebrating in what appeared to be a show of loyalty to the home fans.
His goal rounded off a deserved victory for the npower Championship side who broke the deadlock midway through the first half courtesy of Dutchman Cedric van der Gun.
Shefki Kuqi grabbed a third late on, making up for the penalty he fired against the underside of the crossbar earlier in the evening with the score still goalless.
The League Two visitors settled straight from kick-off and showed they were not to be overawed at the Liberty Stadium, but they were given a let off as early as the 19th minute when Kuqi missed from the spot after Sam Cox had brought down Van der Gun.
And they could count themselves lucky just two minutes later when Kerry Morgan again smashed the Barnet crossbar with an ambitious shot from distance.
But the Bees defence was finally breached as Van der Gun headed home Albert Serran's right-wing cross from close range.
Swansea were more comfortable in possession after the opener, although Barnet were certainly not out of it heading into the second half.
But Brendan Rodgers' side were firmly on the front foot as they went in search of a crucial second, Van der Gun, Morgan and Joe Allen all going close. And the goal finally arrived via Pratley in the 72nd minute as the in-demand ex-Fulham trainee capped a driving run with an unstoppable shot past Jake Cole.
Kuqi missed a sitter from 12 yards as the game entered the closing stages before finally finding the net at the third attempt to round off a successful evening for Swans boss Rodgers in what was his first competitive game at the Liberty Stadium.