Chasing 320, the visitors were bowled out for 191, with Sanderson taking 4-31 to add to his first-innings 5-52.
Tom Taylor (69) prevented a more convincing loss for Derbyshire, who had been 58-6, before Nathan Buck (3-38) accounted for most of the tail.
Earlier, Northants lost their last six wickets for 17 runs to finish 277 all out in their second innings.
Teenage paceman Conor McKerr took 5-54 to end with match figures of 10-141.
Northants' fourth win in six matches strengthened their fourth position in the table and moved them within seven points of third-placed Worcestershire, who lost heavily to Glamorgan.
Derbyshire remain winless in the County Championship in 2017, although they received positive news regarding Luis Reece, who has been discharged from hospital after being taken ill on day one.
Medical staff believe Reece has been suffering from a viral infection, the club said in a statement.
Reece posted on Twitter: "Thank you for all the messages over the past few days. I'm now out of hospital with a short period of rest but all is okay. Thank you again."
Northamptonshire beat Derbyshire by 128 runs in Division Two, with paceman Ben Sanderson again key to their success.