The non-league outfit, who secured their place in the second round with a thrilling win at Rochdale, produced all the drama again as they drew 1-1 at the home of the League One leaders.
Nicky Platt gave United a first-half lead, and, after veteran Brighton coach Mauricio Taricco levelled with seven minutes left, there was still time for United goalkeeper Sam Ashton to save Elliott Bennett's 96th-minute penalty.
United also had Scott McManus sent off.
Another non-league side making a name for themselves were Dover, conquerors of Gillingham in the first round, and victors over Aldershot this time.
Adam Birchall's double, the second a penalty, gave them a 2-0 win, but there was no such luck for AFC Wimbledon, who lost 2-0 at home to Stevenage.
Carlisle left it late to avoid a shock at home to Tamworth, with two goals in the last four minutes giving them a 3-2 win.
Tom Marshall put Tamworth ahead, Gary Madine equalised and Danny Thomas restored Tamworth's lead.
But Francois Zoko (86) and James Chester (90) ensured late heartbreak for the Conference side.
Southampton flexed their muscles witha 3-0 win over Cheltenham.
Luton earned a replay after a thrilling 2-2 draw at Charlton.
Joe Anyinsah gave Charlton an early lead but Andy Drury's brace, either side of Johnnie Jackson's strike, ensured a Kenilworth Road replay for Luton.
Burton got the better of local rivals Chesterfield 3-1.
Scott Rendell scored twice to prevent Wycombe from having an awkward afternoon as they beat Chelmsford 3-1, while under-fire Walsall manager Chris Hutchings came away from Torquay with a 1-0 defeat.
The games between Hartlepool and Yeovil and Notts County and Bournemouth fell foul of the weather, while Peterborough won 2-1 at Bury, Hereford drew 2-2 with Lincoln and David Mooney's goal helped Colchester to see off Swindon Supermarine 1-0.