The Seagulls played at Gillingham for two years until 1999 but had to wait another 12 years before their new Amex Stadium finally opened for business.
They grabbed a dramatic last-gasp win over Doncaster in their first game at the weekend and kept up the tension by making hard work of beating the League Two Gills.
Their manager Gus Poyet was a League Cup runner-up with Tottenham in 2002 and said beforehand he fancies a run in the competition this season.
But they needed a second-half penalty from striker Barnes, after Saturday's two-goal hero Will Buckley was fouled, to squeeze into round two.
Brighton made an unconvincing start with Danny Kedwell, Gillingham's sprightly summer signing from AFC Wimbledon, causing the home defence problems.
Poyet's side began to get on top, though, and strike duo Buckley and Barnes put decent chances wide.
But they survived a scare eight minutes before the interval when Kedwell headed over the top from six yards.
Winger Craig Noone had an opportunity to settle the hosts' nerves in first-half stoppage-time but shanked his effort wide.
Noone took aim again after the interval but Gills keeper Ross Flitney made the save.
At the other end Charlie Lee went close to putting the Kent side ahead but injured himself in the process as Casper Ankergren came out to block and had to be substituted.
But the Seagulls made the breakthrough in the 67th minute when Buckley beat Joe Martin for pace and the Gills defender brought him down in the area.
Barnes stepped up to coolly send Flitney the wrong way and ensure it remains home sweet home for the Albion.