Brigg travelled to defending Lincolnshire League champions Lincoln Moorlands Railway for the first round tie looking for their first win of the season, and so nearly claimed it.
The sides were locked at two goals apiece at half-time and still could not be separated at full-time as the teams shared another four goals.
And extra time failed to produce a result as more goals saw the tie end in a 5-5 draw, only for Brigg to go down 3-1 on penalties.
Substitute Ben Cooke led the way for the Zebras with a hat-trick, while Paul Ashton and Lewis Bazely grabbed the other goals.
Brigg are in more cup action on Saturday when they travel to Nettleham in the Challenge Cup (kick-off 2.30pm).