Goals from Nani, Darron Gibson, Cristiano Ronaldo and Danny Welbeck ensured that a Miles Addison header was nothing more than a consolation for the hosts.
The Rams were able to contain the Premier League leaders for almost half-an-hour before the deadlock was broken.
Both sides had spurned good opportunities by that stage, but there was to be no stopping a 20-yard thunderbolt from Nani.
In an almost exact replica of the goal he scored against Derby in the second leg of their Carling Cup semi-final meeting last month, the Portuguese winger drifted in from the flank before firing an unstoppable effort into the top corner.
That lead was then doubled a minute before the interval when a Ronaldo free-kick broke kindly for Gibson to steer a controlled volley past the stranded Stephen Bywater.
The result was put beyond doubt three minutes into the second period when Ronaldo rose highest to meet a Ryan Giggs corner and power a header into the back of the net.
Derby did snatch a lifeline when Addison glanced home a Kris Commons cross on 56 minutes, but they were ultimately unable to give the Red Devils a scare by forcing a further breakthrough.
It was therefore left to substitute Welbeck to round off the scoring nine minutes from time as he curled a sumptuous fourth past Bywater's outstretched hand.