United States U-21 international Jay Denny struck his second goal of the night and Shrewsbury's third in the first minute of extra-time to clinch a memorable win for the Shrews - and their first of any description this term.
Indeed, it was half-time substitute Denny who had forced an extra half-hour when he fired an 89th minute leveller, just when it seemed Brighton were about to take the tie by a 2-1 margin.
But Denny's extra-time strike was enough to seal a place in round two for the home side - as Brighton suffered a Carling Cup humiliation at the hands of League Two opposition for the second season running.
With both sides still seeking their first league win of the season and each in the bottom four of their respective divisions, it was no surprise that they appeared to lack confidence during an untidy opening spell - but with their first significant attack, the Seagulls went ahead, Mark McCammon heading home a Sebastien Carole cross in the 17th minute.
Six minutes later, however, Shrewsbury drew level against the team standing 44 league positions above them - Mark Stallard crashing home his first goal for the club since joining the Shropshire club in the summer, scoring with an angled drive from ten yards.
There was little to choose between the sides during the second half, but with ten minutes left substitute Jake Robinson looked to have won it for Mark McGhee's side when he met McCammon's cross with a neat side-foot finish.
But at the death Denny blasted in from close range to force extra-time - and then had the last word just 60 seconds into the first period of the additional half-hour, driving a shot low into the Brighton net following good work from Town striker Colin McMenamin.