The Rams had turned around their fortunes before the international break and Nigel Clough's side picked up where they left off at Pride Park.
Dean Moxey opened the scoring with a goal that should have been kept out by Preston goalkeeper Andy Lonergan, it was the former Exeter full-back's first home goal for the Rams.
Derby were dominant in the first half and they were two up at half-time courtesy of a header from on-loan forward Alberto Bueno.
And Rams skipper Savage put the icing on the cake with a penalty after Russell Anderson was brought down by Keith Treacy, who was sent off.
Derby made a bright start and the in-form Kris Commons tried his luck from long range after 10 minutes but the forward's strike flashed over the crossbar.
The Rams looked dangerous going forward with their sharp passing and movement and they were in front after 21 minutes.
On-loan Spaniard Bueno picked out left-back Moxey and his left-footed cross-shot should have been kept out by Lonergan but beat the Lilywhites goalkeeper at his near post.
A minute later the ball fell for Commons in the penalty area and the former Nottingham Forest man's effort was deflected wide.
Derby goalkeeper Frank Fielding, making his debut after being signed on loan from Blackburn on Friday, was tested for the first time 26 minutes in when he kept out Jon Parkin's strike.
But Derby were in control and they doubled their lead after 32 minutes when Shefki Kuqi headed on for the impressive Bueno, who headed home his third goal for the club from six yards out.
Preston were poor in the first half but they looked more threatening at the start of the second half.
Derby still looked threatening going forward and Commons tried his luck twice early in the second half but failed to hit the target on both occasions.
Commons did force Lonergan to make a save after 54 minutes with a free-kick from 25 yards out and the alert Bueno failed to convert the rebound.
Preston then had a spell of pressure and twice tested Fielding.
First Treacy drilled a shot from long range which the on-loan Blackburn youngster palmed away and then Fielding did well to keep out Sean St Ledger's header.
Commons had his best chance of the afternoon with 14 minutes remaining but the former Nottingham Forest man fired wide with just Lonergan to beat.
But Derby had their third goal in the second minute of stoppage time when Anderson was upended by Treacy in the penalty area.
Treacy was shown a red card and Savage stepped up to beat Lonergan from the spot.
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