Richie Towell gave Championship leaders Albion the lead midway through the first half but National League table-toppers Lincoln hit back to win with three second half goals.
Lincoln knocked out another Championship side Ipswich in the last round but it was Brighton who threatened first when Glenn Murray had a header saved inside the opening 60 seconds.
Lincoln's Theo Robinson then had an effort ruled out for offside after eight minutes.
Solly March crashed an effort off the Lincoln bar after an excellent run on 18 minutes, before Brighton took the lead on 25 minutes. Murray flicked the ball on for Richie Towell, who clipped the ball home from 12 yards.
Albion keeper Niki Maenpaa kept out Nathan Arnold's shot at full stretch on 33 minutes as Albion went into half-time with a one goal lead.
The hosts levelled on 53 minutes when Murray was adjudged to have held Robinson back in the penalty area. Maenpaa was injured during the incident and was replaced by Casper Ankergren in goal.
Alan Power slotted home the spot-kick and Lincoln then went ahead on 62 minutes when Brighton debutant Fikayo Tomori turned Arnold's cross into his own net.
Brighton manager Chris Hughton sent on Tomer Hemed and Jamie Murphy for Towell and Jiri Skalak and Albion went close to levelling when Murray's close-range shot was blocked.
Lincoln added a third five minutes from time when Albion gave the ball away and Robinson made it 3-1.
There was still time for Hemed to have a shot saved before Albion failed to find a way through in eight minutes of injury-time as Lincoln progressed into the last 16.
Don't miss out on all the latest breaking news where you live.
Here are four ways you can be sure you'll be amongst the first to know what's going on.
1 Make this website your homepage
2 Like our Facebook page at facebook.com/pages/Sport-Sussex3 Follow us on Twitter @SportSussex
4 Register with us by clicking on 'sign in' (top right corner). You can then receive our daily newsletter AND add your point of view to stories that you read here.
And do share with your family and friends - so they don't miss out!