Burnley had the first chance after six minutes when Youl Mawene fouled Steven Thompson and Graham Alexander played the free-kick to Martin Paterson but his shot was saved.
Clarke Carlisle had a header tipped over in the ninth minute and Preston striker Jon Parkin had a shot saved minutes later.
An out-swinging corner by Chris Eagles on the right wing was headed back across goal to Carlisle and then Chris McCann somehow missed from three yards out.
Paterson and then Joey Gudjonsson had efforts saved.
Ross Wallace had a right-wing corner to the back post which Mawene headed but the ball was cleared and captain Paul McKenna had a left-wing corner which was clawed away.
Just before half-time, Eagles hit a crisp dipping volley from the right wing which Andy Lonergan saved with one hand.
McCann, Jon Parkin and Paterson all had shots saved at the start of the second half.
Stephen Elliott was fouled by Brian Jensen in the penalty area and referee Mr Taylor gave Preston their first penalty which Callum Davidson hit left footed into the left-hand side.
Mawene passed to Wallace and his cross to Richard Chaplow ended in a shot which was saved from eight yards.
Sean St Ledger had a right-foot shot saved just before Burnley equalised in the 76 minute.
Substitute Robbie Blake was fouled by Billy Jones and hit the long range free-kick in off the post into the top left corner.
Eagles had a shot saved and then the referee gave Preston their second penalty when Steven Caldwell hand-balled and Neil Mellor fired home the resulting spot-kick to make it 2-1 late in the day.