Second top flight win of weekend
The 20 points lifted them up to third place — just 13 behind leaders Cavaliers and Carrington.
They both fell on the same score, but number three Harry Ratcliffe struck a top-score of 48 to maintain the momentum.
Ratcliffe hit five fours as he shared three partnerships, including two of note.
First he put on 34 with Tim Wyatt and then 65 with Jack Blatherwick, who struck a six and a four in his 32.
When they were both dismissed, the lower-order kept up the run-chase, taking Papplewick and Linby from 156 for five to 212 for eight and victory.
Daniel Blatherwick and James Taylor both hit 16 with Taylor unbeaten.
Earlier, Gareth Blinkhorn led the wicket-taking with three for 43 from 12 overs.
There were also a couple of wickets for Daniel Blatherwick, while Jim Rhodes and Charlie Blatherwick took one apiece.