Chris McPhee spared Brighton's blushes against third division strugglers Boston in Mark McGhee's first home match in charge.
The young striker scored twice in the first period of extra time to send the Seagulls through to the southern section quarter-finals of the LDV Vans Trophy on the silver goal rule.
McPhee put Brighton back in front on 93 minutes with a shot in of the post.
He ensured only 15 minutes of extra-time were required by scoring again from the penalty spot on 105 minutes after Nathan Jones had been brought down by Lee Beavers.
Richard Carpenter had put Brighton ahead on 23 minutes with a deflected shot, his first of the season.
Boston were rewarded for a brave second-half fightback on 81 minutes when Brighton keeper Ben Roberts was dispossessed by Paul Ellender for Peter Duffield to slot into the empty net.