January signing Smith converted the spot-kick in the 56th minute after Neil Kilkenny had upended Ben Gladwin in the box.
In an uneventful first half with chances few and far between Robins striker Miles Storey spurned a golden opportunity after 29 minutes.
Storey was played in neatly by midfielder Massimo Luongo but saw his shot smartly kept out by goalkeeper Declan Rudd.
Two minutes later the Lilywhites went close through Joe Garner who met a Paul Gallagher cross - but his header was scrambled away by Wes Foderingham.
Mark Cooper's men came out of the blocks emphatically after the break, with both Luongo and Yaser Kasim going close from distance.
After Smith's 16th of the season, Preston boss Simon Grayson responded by making a triple-substitution and his side continued to threaten late on.
Foderingham saved well from substitute Kevin Davies' low drive on 82 minutes, before denying him twice more before the final whistle blew and ended Preston's 12-game unbeaten run.