Milligan netted in the sixth minute only for Steels’ Aaron Moxam to reply instantly.
It took until the 75th minute for Milligan to restore the lead for Bamber Bridge and Alistair Waddecar’s late goal made sure of victory.
The tie of the round saw Clitheroe draw 6-6 at home to Sunderland RCA, with Obi Anoruo hitting a hat-trick.
Kendal drew 1-1 with Selby Town, and hosts Burscough beat Northwich Victoria 2-0.
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In the National League, AFC Fylde continued their unbeaten start with a 0-0 draw at Sutton United.
After going two goals behind in the first 13 minutes, Southport staged a comeback in the second half at home to Ashton United to draw 2-2 in the National League North.
Matthew Ashton opened the scoring in the eighth minute with a 25-yard free-kick and, five minutes later, he provided the pass for Bradley Jackson to head in the second.
A fierce shot by Ryan Astles reduced the arrears early in the second half and Jason Gilchrist got the equaliser in the 74th minute.
But a rugged Ashton side held out for the draw.
In the NPL Premier Division, Lancaster City went down 5-2 at Nantwich Town, where Callum Saunders scored a hat-trick for the home side, and Danny Glover got the other two.
The Dolly Blues’ goals came from Robert Wilson and Sam Bailey.
In the NWCL Premier Division, Charnock Richard won 5-1 at Hanley Town, Joseph Noblet, Alex Ball, Ashley Young (2) and Carl Grimshaw on target.