Wycombe's Matt Ingram saved well from a Tom Clarke header in a poor first half.
It took the hosts until the 83rd minute to test keeper Declan Rudd thanks to Matt McClure's low drive.
Preston could have doubled their lead when Clarke's header was cleared off the line by McClure before Rudd saved late on from Anthony Stewart to ensure their place in the next round.
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Wycombe Wanders manager Gareth Ainsworth told BBC Three Counties Radio:
"It was a world class strike from Kevin Davies that separated the two teams today. You've got to take the positives from that - we haven't been carved apart, we haven't been opened up, I thought we defended very well.
"A little bit of luck would have been good, just to see that ball at the back of the net. We created a lot, but we didn't manage to stick it in the goal.
"Simon [Grayson] has given us a lot of respect and put his full-strength squad out - he obviously wanted to get through.
"I thought we handled it very well. I've got some young kids in there who really performed and shone today, and I'm really proud. I just told the lads - be down, but don't be disappointed about that one, because nobody expected us to win that and we came so close to taking them up to Deepdale."
Kevin Davies' 30-yard volley sealed Preston's place in the FA Cup third round after a scrappy win over Wycombe.