Thomas Webster snared 5-23 and Josh Gillies claimed 3-24 to restrict the hosts to 126 all out.
Askern needed just 22.2 overs to complete victory as Reece Gibbon made 52 and Jeff Morton scored 52 not out.
Barnby Dun were 60-run winners against Hensall in Division Two.
Alex Pepper (75) and Henry Cutts (60) got the visitors up to 241-7 before Hensall were bowled out for 181. James Brooks took 5-35.
Fenwick earned their first win of the season at Glasshoughton as Chris Stothard’s 5-26 limited the hosts to 128 all out. Brad Hunter then made 64 for Fenwick.