A five-wicket success kept Mills in fifth place and enabled them to stay within 17 points of second-placed Sandal.
Nelson skipper Jack Scanlon (86) was the only player to reach double figures as his side were bowled out for 150.
Khan (5-43) posed the main threat for Mills while Usman Maqsood bowled 15 overs and took 2-44.
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An early blip saw the visitors reduced to 19-2, but they recovered to reach their target in comfortable fashion with Sohail Hussain (45) top scoring. Umar Abbas (22no) and Imran Patel (21no) saw them home.
Despite a good effort to chase down a big score Hartshead Moor lost by 24 runs to Sandal.
Danny Riley (92) and Karl Hewitt (34) led the way as Sandal scored 283-6.
Overseas player Abishek Paradkar threatened to make light of the target set as he scored a 77-ball 71. Support came from Martin Ellis (25), Joe Bowman (25), William Walker (23no), Craig Field (22) and Josh Marsden (22), but they were unable to turn promising starts into a big knock and Moor ended on 259-9.
Liversedge’s run of 11 straight wins in Division Three was ended when Heckmondwike & Carlinghow inflicted a first defeat of the season on them.
Chris Allen (4-16), Muhammad Shahnawaz (3-35) and Wasim Khaliq (2-32) combined to bowl the leaders out for 135 as they fell 16 runs short when chasing Heckmondwike’s 151.
Only Parvaise Khan (34) and Adam Clarke (29no) were able to make much impact.
In the low scoring contest Hamza Shahzad’s 33 and Fahad Imam’s 30 proved important for Heckmondwike.
Bradley Drake (3-46) was the most successful bowler for Liversedge who remain 28 points clear at the top despite the loss.
Bottom of the table Crossbank Methodists went down by seven wickets to promotion-chasing Adwalton.
Only three batsmen were able to reach double figures – Theo Hanson (16no) and Mohammed Usman (16) top scoring – as Anas Imtiaz (5-42) and Adam Holroyd (4-46) combined to bowl them out for 100 and Adwalton eased to their target in 19.3 overs.
Scholes maintained their promotion challenge with an 83-run win over Rodley.
Adam Greenwood (76) hit 12 fours, while Joshua Fell and Nick Firth both contributed 46 to help the third-placed side to make 273-7.
Rodley were all out for 190 in reply as Adam Greenwood (3-9), Hamza Khan (3-46) and Mahleb Mahmood (3-58) wrapped up victory for Scholes.
Bilal Ejaz (96) and Alex Leadbeater (54) shared a second wicket stand of 109 to help propel Spen Victoria to a five-wicket win over East Leeds.
Ejaz smashed 18 fours in his 58-ball knock then Ayaaz Ali (31) and Paolo Girardi (31no) built on the good work to see the team past East Leeds’ 230 score.
Rahat Shah (4-70) had been Spen’s best bowler.