The Rams hit the front in the 28th minute through Jerry Yates' expertly taken finish for his first goal in six matches but West Brom were twice denied by a post in the first period as Derby took a lead into the half-time interval.
Mason Holgate deflected into his own net from Kayden Jackson's strike to give Derby breathing room, but nerves grew inside Pride Park when Grady Diangana scored his first goal since March in reply.
The hosts held on to deal the Baggies a fourth defeat of the campaign, a relief for Warne after Derby let in two late goals in the recent loss to Luton.
He said: "Second half when they put it on us, we hung in there and defended pretty well.
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