The lively Stephen Dobbie, who spent the second half of last season helping Blackpool win promotion, opened the scoring with a well-taken finish in the 23rd minute.
Darren Pratley pounced from David Cotterill's corner to grab a second goal, displaying his stated desire to focus on his football after a turbulent couple of weeks regarding his future. Nathan Dyer then added a third before the break after a well-worked move.
It got no better for North End in the second half as Cotterill, who impressed in midfield, added a fourth from the penalty spot for a Swansea side who saw a severe lack of goals derail their promotion bid last term.
The victory and manner of the performance would certainly have delighted Rodgers who watched his side go down 2-0 at Hull last weekend.
In stark contrast, opposite number Darren Ferguson will have been furious with the way in which Preston have lost their opening two league games for the first time since 1989/90.
Scott Sinclair, a midweek record signing from Chelsea, enjoyed a superb Swansea debut on the wing while Premier League target Angel Rangel returned at right-back after a thigh injury.
Ferguson made just one change to the starting XI after the 2-0 loss at home to Doncaster on the opening day, with midfielder Adam Barton coming in for Darel Russell.
A moving minute's silence was observed prior to kick-off in honour of Swansea striker Besian Idrizaj who passed away over the summer following a heart attack at the age of just 22.
The 14,010 inside the Liberty Stadium witnessed an end-to-end opening quarter in which Swansea midfielder Cotterill almost broke the deadlock when his drive rebounded off a post.
But City fans did not have to wait long for the opener as, within a matter of seconds, Alan Tate regained possession and fed Dobbie who fired into the bottom corner from a central position just inside the penalty area.
North End were second best after the opener as the hosts gained the upper hand and it was 2-0 in the 40th minute.
Cotterill's corner was flicked on by Garry Monk and then Ashley Williams before Pratley punished the visitors' woeful defending by finishing from close range.
And the game was over as a contest before half-time as Cotterill found Dobbie with a reverse pass and he squared the ball across the face of goal for Dyer to convert from six yards.
Preston boss Ferguson must have dished out hairdryer treatment more associated with his father at the interval as his side emerged for the second half well ahead of their hosts.
But it seemed to make little difference as Swansea went close to adding a fourth goal within a minute of the restart through Sinclair, Pratley and then Dyer.
Yet the fourth was soon on its way as Keith Treacy brought down Dyer in the penalty area and Cotterill converted the resulting spot-kick.
Swansea went in search of a fifth, occasionally leaving the visitors free to attack - Treacy hit a post in the closing stages - but the goal glut was over, leaving North End still waiting for their first victory at Swansea since 1963.