No play was possible on the second and final attempt of the scheduled first-round replay at The Mardyke.
A remote bowl-out was needed to decide who would progress with the Munster side missing all five attempts.
Cameron Rowe was the Balbriggan hero as he hit on the second attempt to book their place in the last 16.
There they will have a home tie against North Down at Jack Harper Park on Sunday June 9th.