Derby's biggest victory for several seasons boosted their chances of staying up but manager George Burley remains cautious about their survival prospects.
His team now have 49 points but Burley said: "I have said that we will need 52 or more points so we need at least one more win if not two. It's still going to be touch and go." Preston have no such worries although manager Craig Brown issued an apology to the travelling fans after an abject first-half display.
He said: "I feel embarrassed and every player and everyone associated with this club does as well.
"I can only apologise to the Preston supporters and I guarantee there will not be a repetition of this kind of stuff next season." Brown also admitted his team had failed to show up in the first half when they were pulled apart by a committed and determined Derby team.
Spanish striker Manel and Marcus Tudgay both scored twice to give the home side a four-goal cushion.
Although Derby were less convincing after the break, Preston could not narrow the margin enough to pray on any nerves and a late penalty restored Derby's advantage.
In recent weeks, Burley has complained that the luck has deserted his team but there was an element of good fortune about the opening goal when a ricochet went in off the shins of Manel.
The second was down to quality approach play with Tudgay placing a left-foot shot inside Jonathan Gould's left-hand post from ten yards after Manel had set him up.
Tudgay scored again when Manel's 20-yard shot came back off the bar and the Spaniard was on hand to put away the rebound when Gould could only parry a 20-yard free-kick from Tom Huddlestone.
Preston at least made a better fist of things after the break with Chris Lucketti heading home via Youl Mawene when Paul McKenna crossed from the left.
Dickson Etuhu and Richard Cresswell then wasted good chances before Lucketti was penalised for a handball in the 75th minute.
The decision looked harsh but Brazilian striker Junior sent Gould diving to his right before placing the ball to the keeper's left for his first goal since he returned from a serious knee injury.