The relegated Rams have now lost 26 leagues this season, with goals from Bobby Zamora and Carlton Cole ensuring Tyrone Mears’ effort was just consolation.
The Hammer took the lead on 20 minutes, when George McCartney’s free-kick was headed home by Zamora, who had another goal ruled out for offside on 37.
Mark Noble drew a good save from Roy Carroll, while at the other end Robert Green tipped a goalbound header from Robbie Savage over the bar on 38.
After the break, Green bravely denied Mears on 62 but was beaten on 65 when the Rams right-back finished coolly with his right foot.
The hosts had the last laugh, though, as Cole tapped in from close range after good work by Freddie Ljungberg on 77.