Davies, who was playing for England just over three years ago, swivelled on the right-hand side and sent his effort dipping over Matt Ingram in the Wycombe goal in the 34th minute.
The 36-year-old's third of the season extended his side's unbeaten run to 10 games, in stark contrast to Wycombe who now have only one win in 11.
With both managers opting to play five in midfield neither side found much fluency in a tight first half that was only brought to life thanks to Davies' superb volley.
Ingram saved well from a Tom Clarke header as the home side struggled to create any clear cut chances of their own during the opening 45.
Things only marginally improved for Gareth Ainsworth's men after the break and they took until the 83rd minute to test 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 Preston's place in the third round.