After a tight first quarter which Bullets edged 22-19 on a steal and a dunk by Justin Phoenix, the Storm looked short of an alternative when their run-and-gun offence dried up.
Three-pointers from Chris Fite and Kip Stone were Derby's only counter to a 19-8 Birmingham run which took them to the biggest spread of the night at 41-27.
Then Bullets dried up and only Nigel Lloyd, from the foul line, and the sixth man, Emiko Etete, added to their score before half-time.
Bullets steadily lost the plot. Centre Shawn Jamison, enraged by a call against him, earned a technical foul in addition and handed Carl Miller three free throws as Derby cut the deficit to 45-40 at the break.
Derby's rookie but increasingly confident coach, Martin Ford, took his cue from the Bullets' nervous end to the half and on the restart threw a full court press at Lloyd, Lee Walker and the former Derby man Yorick Williams.
Once two baskets from Evans had given Derby a 60-56 lead the momentum stayed with them. The Bullets challenge petered out as Jamison, inevitably, and Phoenix fouled out in the fourth, leaving the imperturbable Miller to calmly seal Derby's place in the last eight from the foul line.
Derby join Sheffield Sharks, London Leopards, Manchester Giants and Newcastle Eagles in the last eight with the remaining places to be settled next weekend.Reuse content