Juvhel Tsoumou had put Preston ahead but three second-half goals in 20 minutes from Wesley Thomas, Scott Malone and Pugh gave Lee Bradbury’s men all three points.
Preston took the lead after 29 minutes when in-form forward Tsoumou turned sharply in the six-yard box to finish smartly after Bournemouth failed to clear.
The Cherries equalised after 48 minutes when Thomas latched onto Pugh’s pass and slotted home his sixth of the season after rounding Iain Turner.
Bournemouth then took the lead before the hour when Malone, on loan from Wolves, notched his first for the club with a cool finish at the second attempt from 10 yards.
Pugh scored Bournemouth’s third after an awful mix-up between Clarke Carlisle and Turner left him with an empty net to pass into. Darryl Flahavan made two fine stops to keep Preston out late on but the Cherries never looked in danger.