Preston opened the brighter team with Barry Nicholson having an in-swinging corner headed by striker Chris Brown but straight at Swansea keeper Dorus de Vries.
Brown had a great effort in the seventh minute when he hit a six-yard right-foot shot against the post and Preston captain Paul McKenna had an 18-yard shot from inside the right channel which was caught by the keeper.
Swansea's Ferrie Bodde latched onto a loose ball and hit a 45-yard thunderbolt into the top left corner to make it 1-0 to the Welsh side after 19 minutes.
Nicholson had another corner from the left wing which he took right footed but it was caught by the keeper and Jordi Gomez had a 25-yard free-kick from the right wing which was tipped over the bar by Andy Lonergan.
Just before half-time, Mark Gower found Gorka Pintado with an inch-perfect cross and his 12-yard header was saved by the Preston keeper.
Nicholson had another cross saved by the Swansea keeper and Jay McEveley had a cross claimed by de Vries.
McEveley had another cross caught by the Dutch keeper and then substitute Ross Wallace had an 18-yard left-foot shot from inside the left channel saved.
McKenna had a right-foot free-kick from the left punched away by the keeper.
Nicholson crossed the ball to Wallace and he had a left-foot shot from the left-hand side of the penalty area which was parried by the keeper.
With ten minutes to go, McEveley tripped Gomez in the penalty and the referee had no hesitation in giving Swansea a penalty.
Gomez stepped up to hit a left-foot penalty into the top right to make it 2-0.
Towards the end, Preston striker Neil Mellor had an 18-yard shot tipped around the post by the Swansea keeper.