New signing Ben Pringle scored twice and assisted two more for a Derby side that blended youth and experience against the Northern Counties East Premier Division opposition.
Jermaine Johnson, Alexsander Prijovic and Henrik Ojamaa also scored.
"I thought Ben stood out," Rams coach Gary Crosby told the Derby Evening Telegraph.
"The quality of his crossing, the quality of his two goals and his general work-rate and application was very good.
"But I thought the attitude of all the players was spot on from the very first whistle.