Hallam booked their place in the first round of the FA Vase with a 1-0 in at Bootle.
Micah Bishop netted the only goal of the game with a deft header nine minutes from time to secure Hallam's win over the North West Counties League side.
“I thought we controlled the game from start to finish, barring 15 minutes, which is tremendous against a team from a league above us,” Hallam assistant boss Dean Bamforth said.
Alex Lill scored a hat trick as Swallownest also eased through the second qualifying round with a 4-1 win over AFC Blackpool.
Lill fired Swallownest ahead on seven minutes after Blackpool had threatened early before he added a second on the quarter hour.
Josh Lill made a superb save to deny Blackpool before Alex took centre stage again, completing his hat trick just after the hour mark with a fine finish from an acute angle.
Blackpool pulled a goal back on the hour but any hopes of a comeback were quickly snuffed out when Alex Layne added a fourth for Swallownest 15 minutes from time.
Staveley MW also secured their passage with a 4-1 win over Maine Road.
Jahmal Riley gave the Trojans the lead inside two minutes only for Maine Road to quickly equalise.
Liam Greenfield restored the advantage for Staveley before the break before Riley put them in full command with his second early in the second half.
Sam Finlaw added a late fourth.
Dronfield Town came from a goal down to beat Harborough Town 3-1 to reach the first round proper.
Callum Mawbey, Matt Ord and Mark Fereday all netted within 14 second half minutes to see Dronfield through.
Parkgate exited the competition with a 3-1 defeat at Glasshoughton Welfare.
Worksop Town are also out after losing 5-0 at Winsford United while Rossington Main were beaten 2-0 by Winterton Rangers.