Tom Lace (48*) and Wayne Madsen (41*) rebuilt for Derbyshire to take the visitors to 97-2 at the close, leading Gloucestershire by 38 runs.
Earlier the hosts were all out for 350 as Gareth Roderick top-scored with 98 and Luis Reece claimed 3-60.
Reece and Billy Godleman fell early in the Derbyshire reply, but the experienced Madsen and the young loanee Lace batted well to the close and will resume on the final day looking to build the lead.
A winning start! Derbyshire start the 2019 season with a victory. Never miss a moment this summer with Club Membership. Buy online or call 01332 388 101.