Struggling Shrewsbury spent much of the first half on the front foot as they caused Preston problems.
Tom Eaves, the striker on loan from Bolton, bulldozed his way through two challenges only to be denied by Preston goalkeeper Declan Rudd at the foot of his near post.
Then little winger Jon Taylor cut in from the left and tried his luck with a well struck 20-yard drive which Rudd did well to palm away.
Preston carried little threat although David Buchannan did crack one shot on the turn just wide with home goalkeeper Chris Weale scrambling.
The second half was a more even affair with Joe Garner and Paul Huntingdon both off target with headers from corners, while at the other end Luke Summerfield blazed Adam Reach’s inviting cross over.
Deadlock ensued until 11 minutes from time when Preston substitute Ian Hume burst clear down the right and his low cross was turned into his own net by young right-back Woods.
Shrewsbury have now lost four home games in a row, but Preston have no such problems as they continue to chase promotion.