Preston dominated the ball in the early exchanges, but aside from a Paul Gallagher strike - which deflected wide of the Derby post - opportunities were few and far between in the first 20 minutes of action.
The home side had a golden chance to take the lead in the 37th minute when Derby defender Andre Wisdom was adjudged to have brought Alan Browne to the ground inside the box, but the Preston midfielder rose to his feet before sending the penalty against the outside of the post.
It was Derby that took the lead in the 52nd minute, with Lawrence's free kick from distance somehow finding a route into the bottom corner for his fourth Championship goal of the season.
The visitors had the opportunity to double their lead just past the hour when Andreas Weimann's deep cross looked to be finding David Nugent, but the striker could not make contact at the final moment.
Paul Huntington then passed up a good chance for Preston down the other end when he fired over the crossbar having been presented with space inside the Derby box.
Kasey Palmer might have wrapped the points up for Derby 10 minutes from time when he broke into a shooting position, but the substitute sent the ball wide of the post.
Gallagher then fired over the away side's crossbar five minutes later following a mistake from Scott Carson.
Preston, who remain two points off the playoff positions, threw everything at Derby in the latter stages, but Gary Rowett's side held on to secure all three points.
PRESTON (4-2-3-1): Maxwell; Fisher, Huntington, Davies, Cunningham; Gallagher, Pearson; Robinson (Johnson 79'), Browne (Moult 63'), Barkhuizen (Bodin 73'); Maguire
DERBY (4-2-3-1): Carson; Baird, Pearce, Davies, Wisdom; Huddlestone, Ledley; Weimann, Vydra (Palmer 74'), Lawrence (Hanson 89'); Nugent (Jerome 90')