Goals from Lance and Niall Johnson, and sub Oliver Thomas took the Division One side through.
In East Lincs Combination Division Two, Sutton Rovers were handed an away walkover at leaders Manby.
Title-chasing Alford Town were held 1-1 at Division Three outfit Market Rasen in the Town Trophy quarter-finals.
Corey Lewis’ second-half strike ensured Alford will go into the second leg on level terms.
Selected fixtures (Saturday) –
Division One: Louth Old Boys v Grimsby Borough Dev A; Louth Town Res v Immingham Town Res.
Division Two: Alford Town v Scamblesby.
Division Three: Alford Town Res v Burgh Athletic.
Town Trophy quarter-final second leg: GB Kitchens v Sutton Rovers (Sutton lead 4-2).