Tommy Treacher converted two penalties as Long Sutton Athletic booked their last-16 place.
Matty Oliver was also on the Magpies’ scoresheet at home to Coningsby on Saturday.
The 3-2 win set up a trip to Sutton Rovers next month.
Moulton Harrox have been drawn at home to Ruston Sports following last week’s 5-2 win at Sherpa.
Tydd St Mary were beaten 2-1 at home to Crowle Town Colts on Saturday.
Crowland Town crashed out 5-0 at Wyberton as Adam Abell (2), Jamie Elston, Curtis Revell and Curt Yeatman got the goals.
Third round draw (to be played November 4, 1.30pm kick-off): Epworth Town v Shape Changers, Wyberton v Crowle Town Colts, Sleaford Sports Amateurs v Limestone Rangers, Appleby Frodingham v Skegness Town, Sutton Rovers v Long Sutton Athletic, Moulton Harrox v Ruston Sports, Barnetby United v Tetney Rovers, Spilsby Town v Lincoln Moorlands Railway.