Billy Jones fouled Mark Gower and Preston goalkeeper Andy Lonergan caught Jordi Lopez's inswinging free kick after 13 minutes.
De Vries saved an Eddie Nolan cross after 15 minutes and Swansea winger Gower's 17th minute shot from the left went over the bar after hitting Lonergan's foot.
A cross by Wallace after 24 minutes was saved and then Preston scored in the 27th minute.
Chris Brown assisted and Neil Mellor from the left headed into the far corner from seven yards for his fourth goal of the season.
Parry beat the Swansea full-back in the 32nd minute and his shot was saved for a corner.
Nathan Dyer volleyed Gower's cross to the near post but the ball was saved in the 37th minute.
Sean St Ledger fouled Swansea winger Dyer in the 38th minute and was booked.
In the second half, Ashley Williams fouled Brown and was booked in the 49th minute.
Nolan's three-yard effort from Parry's cross was saved after 50 minutes.
Lee Trundle was replaced after 56 minutes by former Preston loan player Craig Beattie.
Chris Sedgwick made his 200th league appearance for Preston as he replaced Wallace and Cedric van der Gun made his Swansea debut as he replaced Lopez after 62 minutes.
Parry injured his left leg and was replaced by Veliche Shumulikoski.
Gower found Beattie and his deflected shot was saved at the near post by Lonergan's legs in the 70th minute.
Painter was booked for a foul on Sedgwick after 71 minutes.
Jones' effort was saved after Sedgwick's right-wing cross after 75 minutes.
Gorka Pintado replaced Painter and Stephen Elliott replaced Mellor after 80 minutes.
Preston made it 2-0 after 89 minutes when a Sedgwick cross from the touchline was volleyed home from a tight angle by Elliott from six yards into the top right.
Ashley Richards and Elliott were booked in the 90th minute and Elliott and Shumulikoski had shots saved in added time.