Jacob Mason put the home side ahead, in one of only three North Division games to beat the weather, after just five minutes.
Jordan Livett found the net on 58 minutes when doubling Harworth’s lead.
Josh Davies put paid to any comeback hopes that the visitors might have entertained when adding a third on 81 minutes.
But Askern battled to the end and pulled a goal back through Ash Evans two minutes later.
Premier Division strugglers Yorkshire Main booked their place in the final of the Doncaster Rovers Senior League’s Challenge Cup final in May, where they will meet Rum Rooms Legacy at Rossington, when beating Division One hosts Doncaster Town by the odd goal in seven.
Ricky Caudwell, Reece Davis, Andrew Kyme and sub Kieran Falcus were the Main marksmen.
Doncaster Deaf and Bridon AFC battled out a 2-2 Division One draw in the only other game played.
Mathew Durham and Nick Spires both netted first half goals for the visitors who led 2-1 at the break.