The midfielder opened the scoring in the 10th minute and struck again midway through the second half to reawaken City's relegation fears.
A sixth away victory of the season was no more than Brendan Rodgers' high-flying side deserved as they created chances throughout and forced several fine saves from former England goalkeeper David James.
City handed a debut to striker Andy Keogh who joined on loan from Wolves on transfer deadline day.
Swansea midfielder Leon Britton started for the first time since his return from Sheffield United, replacing Joe Allen in front of the back four, while Mark Gower replaced Kemy Agustien in midfield.
Swansea striker Luke Moore engineered the space to hit a shot from 20 yards in the second minute.
His effort was blocked by Steven Caulker but City threatened moments later when Keogh was given the time and space to strike a shot from distance which Dorus De Vries saved comfortably.
Yet the visitors struck the opening blow moments later when Pratley opened the scoring in the 10th minute.
The midfielder collected a pass from Moore and hit a superb 18-yard right-foot shot into the top left-hand corner.
The hosts sought an immediate response but Marvin Elliott fired narrowly wide from 25 yards.
Moore was proving a constant menace for Swansea and in the 19th minute he almost found the net when he fired goalwards from six yards.
His effort was blocked by Damion Stewart and Moore went close with a fine 25-yard shot which drew a superb parried save from David James.
Keogh then headed straight at De Vries at the other end before Pratley fired over James' goal from the edge of the 18-yard box.
The momentum remained with Swansea after the restart as Scott Sinclair fired goalwards from 25 yards with a fierce strike which warmed James' hands.
Pratley then rifled a shot wide and Swansea defender Ashley Williams blazed over the crossbar from just six yards out.
Moore then had another shot blocked by the overworked James but the hosts should have been level in the 65th minute when Albert Adomah headed wide from 12 yards.
Two minutes later, his wastefulness was punished as Pratley claimed his second of the night and ninth of the campaign.
An inswinging corner from Gower fell to Pratley and he swept the ball home right-footed from six yards out.
Nathan Dyer then hit a shot just wide and James saved well from Pratley as he went in search of his hat-trick goal.