Haseeb Hameed made 93 and Ben Slater 64, the openers sharing an unbroken partnership of 167 to see their team home within a single session - albeit one extended by almost 20 minutes to avoid the players having to return after lunch.
Derbyshire, meanwhile, suffered their first defeat under the stewardship of new head coach Mickey Arthur, although given their depleted bowling ranks they always faced a tough task against a strong Nottinghamshire line-up.
Two of the bowlers due to start this match, Suranga Lakmal and Anuj Dal, dropped out injured at the 11th hour, Dal as late as Thursday morning, after the original team sheet had been submitted. Another, Luis Reece, suffered a groin injury after bowling less than nine overs in the first innings.
Nottinghamshire opener Hameed, who scored an unbeaten 93, said: “It is always nice to contribute to a winning performance. It would have been nice to turn it into another hundred but it was one of those situations where if it happens, it happens, and I was just happy to be there at the end with Ben.
“We are moving fast as a team. We had our one blip here against Glamorgan and I think that served as a reminder to us to keep doing what we have been doing over the last 18 months, a period in which I think we have progressed a lot.
“We took a lot from the performance at Lord’s last week when we performed well over the four days, even though we were foiled by rain in the end.
“Myself, I’m pleased with the way I’m playing this season. I just try to keep improving and adding things to my game, playing a bit more aggressively. Right from the start of my career, when people used to kind of pigeon-hole me as a certain type of player, I was clear that I was always looking to develop and get better and that hasn’t changed. As I get older and a bit more experienced, that aggression comes out more naturally.”