Fairbank booked a date against Park in the Wilf Ward Memorial Trophy final after ending the hopes of West Bradford Spartans 5-2 in the Spen Valley League knockout competition.
Danny Davey netted both Spartans goals, including one in the opening minute, and it was 2-2 at the interval but Fairbank then pulled clear.
There were league games in midweek and on Saturday and Oakwell closed in on the Premier Division title with a 7-1 win against Bradford, including a Jason Elliott hat-trick.
Nearest rivals TVR United beat Ravensthorpe Rangers 7-3 but then slipped up as third-placed Wellington held them to a 1-1 draw.
Spartans are in pole position to clinch the Division One title after wins against Park (6-1) and Howden Clough (4-3).
Other Division One results: Inter Batley 1, BD3 Utd 3; BD3 Utd 3, Marsh 2; Norfolk 2, ALC 3; Oakwell Res 3, Fairbank 6; Stithy 1, Park 7.
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