Fletcher took match figures of 8-64 to top the County Championship bowling charts as Notts eased to an innings and 36 run win over their struggling neighbours.
It leaves Notts top of Group One in the LV=Insurance County Championship with one match remaining of the group stage as they bid to clinch a place in the Championship division.
“Apart from taking wickets myself, I’m buzzing that we got a victory, a massively important result to put us top of the table, because we’re desperate to get into that top division,” said Fletcher.
“I was a bit worried how this game would go after T20 but after four or five overs I slotted back into my rhythm.
"The good thing in four-day cricket is that you can get into your spells, which I think we’ve done as a bowling group and got better as the game went on - it was a great team effort.
“Everyone is stepping up at different times and contributing, and you’ve seen Dane Schadendorf come in for his debut today.
"He was very calm and relaxed and looked like he belongs. As a wicketkeeper you didn’t really notice him, which is always a sign that he was doing everything right.”
Nottinghamshire had been all out for 307 in reply to Derbyshire’s first-innings 149.
Ben Duckett’s 69 not out overnight remained the top score despite the left-hander having to be replaced mid-innings after England’s Covid emergency saw him called him.
The withdrawal of Duckett, who had been keeping wicket because Tom Moores is unwell, meant a senior debut for Dane Schadendorf.
Nottinghamshire added 51 to their overnight lead of 107 before Derbyshire claimed the last three wickets.
Derbyshire lost Tom Wood in the seven overs before lunch as he edged Fletcher to first slip, before Brooke Guest was caught behind. Wickets in consecutive overs from Dane Paterson plunged Derbyshire into more trouble, before Leus du Plooy and Luis Reece were out.
Derbyshire continued to crumble and lost their last four wickets inside 12 balls.