Martyn Waghorn came off the bench to score the goal that secured a 1-0 victory for Derby over Preston.
Waghorn diverted the ball in from close range in the first half and Derby could have had more goals against a strangely subdued Preston who created little.
Phillip Cocu's side made a confident start with Lawrence firing narrowly wide from distance in the fifth minute.
Derby had to make a change in the 15th minute when Graeme Shinnie appeared to suffer a hamstring injury and was replaced by George Evans but the home side went close twice in the space of two minutes.
First Duane Holmes rattled the bar with a volley before Lawrence broke away in the 19th minute and hit a low drive which Rudd turned behind.
Bennett limped off in the 28th minute and his replacement Waghorn had a great chance three minutes later when Holmes put him through but Rudd turned his shot over.
But Waghorn was in the right place in the 33rd minute when a corner was headed on and he chested it past Rudd from six yards.
Preston could have no complaints because they had been second best but Derby had a scare in stoppage time when Kelle Roos dropped a free kick but the visitors could not take advantage.
Derby had another chance in the 54th minute when Krystian Bielik's pass put Waghorn in but his shot was easily saved.
Preston had the ball in the net three minutes later but the flag was up for offside and Jayden Bogle was close to adding a second with a shot that went just wide in the 64th minute.
But Derby were dropping deeper and had a scare in the 77th minute when a free kick dropped to Barkhuizen who grazed the bar with a 15 yard shot.
Preston dominated possession in the closing minutes but could not fashion a clear chance as Derby held on for a fifth successive Pride Park victory.