Fulwood, who finished second in Division One Reserve, took an early lead against Hesketh Bank through Cory Gill.
But Bank, who ended their Division Two Reserve campaign in fourth, hit back in the second half through John Stead's effort.
No further goals arrived in normal time so it went to penalties where Fulwood prevailed 3-1.
The cup follows on from the first team's Lancashire FA Shield win on Tuesday and news that club stalwart Tony Hesketh was stepping down from managerial duties.
See Paul O'Brien's match gallery HERE
Keep up-to-date with our exclusive email newsletters.
Subscribe