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Despite outplaying Derby for most of the game, the Baggies were punished when the Rams struck twice in the space of four minutes.
An unstoppable 25-yard shot from Matty Oakley levelled the contest in the 69th minute before Giles Barnes headed his fourth goal in three games.
All West Brom had to show for there superiority was a 26th minute goal from Richard Chaplow but they should have scored at least two more.
Derby were completely outplayed in the first half but West Brom failed to make the most of their possession with Chaplow missing a great chance in the 18th minute before skipper Curtis Davies struck the crossbar after Stephen Bywater had fumbled a free-kick.
Chaplow did find the net when a pass from Nathan Ellington was deflected into his path and that should have put the visitors on course for a convincing win.
If Ellington had scored in the 46th minute instead of shooting wide of a gaping goal the match would have been out of Derby's reach.
Diomansy Kamara wasted another opening when he fired into the side-netting and the warning signs for West Brom started when Steven Howard headed against the outside of a post.
West Brom were on the attack when Zoltan Gera lost the ball and Oakley surged forward before unleashing a 25-yard drive that flew into the top right-hand corner of the net.
Three minutes later Chaplow needlessly gave the ball away and Morten Bisgaard crossed for Barnes to head the winner from eight yards.
With the match slipping away, West Brom piled forward but Bywater made a couple of vital blocks in a frantic period of stoppage time before Derby were able to celebrate another great escape.