Tom Craddock had put Luton ahead just two minutes into the southern final second leg at Kenilworth Road, but Nicky Forster levelled for the Seadulls on the 20 minute mark.
When the tie went to penalties after 90 minutes - there was no extra-time - two stops from the Luton keeper Lewis Price proved decisive.
Luton are rooted to the foot of the League Two table with just two points to their name, having started the season on -30 due to financial misconduct of previous owners and failing to satisfy Football League rules on insolvency.