Ole Gunnar Solskjaer ensured his squad got a proper run-out but still secured a positive result, with Tahith Chong and Facundo Pellistri scoring the goals, both from the right-wing berth.
Colin Kazim-Richards pulled one back on 70 minutes but the Reds were worthy winners in sweltering conditions at Pride Park, in front of a noisy band of travelling supporters.
FIRST HALF - CHONG ON TARGET
Debutant Tom Heaton soon showed his worth in goal with a top-drawer save to deny defender Curtis Davies as the Rams settled quicker in the warm temperatures. The Reds started to gain some control, with left-winger Anthony Elanga often an outlet with his pace causing problems.