It was a woeful display from the Rams, who could have climbed out of the relegation zone had they picked up only their second win of the season.
As it was they were lucky to escape with just a 5-0 drubbing as the Hammers ran riot, twice hitting the woodwork and creating a hatful of other chances.
There was little to suggest what lay ahead in an injury-marred first half in which Derby held their own, without ever looking like scoring.
When the goal came it was West Ham who took it having wasted several earlier openings.
Nolberto Solano had hit the bar with a superb 20-yard free-kick before man-of-the-match Lee Bowyer gave West Ham the lead they richly deserved.
Solano's cross was headed down by Carlton Cole and Bowyer ran unmarked into the box to slide the ball home.
The opening minutes of the second half was a nightmare for Derby as West Ham created chances at will.
Luis Boa Morte was unlucky not to score in the 46th minute and from the resulting corner Matthew Upson rattled the Derby woodwork.
Then three goals in just eight minutes put the game beyond doubt.
Kenny Miller had missed Derby's best chance, squandering a free header, before West Ham put the matter beyond doubt. John Paintsil found Matthew Etherington in the box and after a clever one-two with Bowyer, Etherington swept the ball home.
A minute later Jonathon Spector saw his goalbound shot carried over the line by the unfortunate Eddie Lewis for an own goal.
Bowyer then ran through unmarked on the hour to score number four after Solano played in Cole, who neatly crossed into the midfielder's path.
With the game won West Ham indulged in some passing football as Derby desperately tried to salvage some pride.
But there was worst to come on 68 minutes when Solano curled another delightful free-kick into the net, beating both the wall and the keeper from 20 yards out.
Derby had no response to West Ham's movement up front with Cole and Boa Morte showing the sort of class that Derby so desperately need if they are to retain any hope of staying in the top-flight.