Preston picked up their first win of the season and it left home fans calling for Davey's head with the new term just three matches old.
Two first half strikes from Paul Parry and Neil Mellor put the visitors in control and when Barnsley-born Jon Parkin rattled in the third, it was too much for many Tykes fans.
Barnsley, with only a point from their impressive first day draw at Sheffield Wednesday, were looking to bounce back from their dismal defeat at home to Coventry on Saturday.
They had a promising opening when right back Bobby Hassell overlapped and produced an accurate cross but striker Kayode Odejayi's powerful header was over the top.
Canada international Iain Hume, in his first start since fracturing his skull in November, whipped in another cross but Stephen Foster headed over.
In Preston's first attack of note, Billy Jones broke with pace down the right and his perfectly weighted pass sent Paul Parry cutting into the area.
The ex-Cardiff midfielder, kept his cool and outwitted home keeper Luke Steele by drilling a sensational shot inside the post from eight yards, providing an early birthday present for himself a day before turning 29.
Preston looked vulnerable as Barnsley went hunting for a quick reply and keeper Andy Lonergan had to palm out a splendid cross from Hume on the right.
Luke Potter's shot was deflected wide after Jamal Campbell-Ryce swung in a cross before Odejayi headed over.
But after 32 minutes Preston broke with purpose again and as the Barnsley defence was caught flat footed, the ball dropped into the area for Neil Mellor who struck a sweet volley for his second goal of the season.
Parkin rounded off the rout in the 72nd minute when Billy Jones swung in a super cross and Parkin, unmarked, chested down superbly and lashed in the shot from eight yards.