Victory was Notts' third from five games so far, inflicting a second straight loss on Leicestershire.
After Notts put the Foxes into bat, Mark Cosgrove (80) was the visitors' top scorer as James Pattinson (4-42) helped restrict their total to 217.
Samit Patel (79) put Notts on course and half-centuries from Brendan Taylor and Steven Mullaney saw them home.
Having initially started their chase by losing Michael Lumb to the first ball of their reply, victory saw the Outlaws leapfrog the Foxes into third in the North Group table.
Leicestershire lost five wickets for just 15 runs between their 35th and 39th overs, as only Cosgrove passed 40 for the visitors.
Nottinghamshire chased down 218 to win with 11.4 overs to spare as they beat Leicestershire in the One-Day Cup.