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 keeper Sam Ashton to save Elliott Bennett's 96th-minute penalty.
United, who also had Scott McManus sent off, will now take their place in Sunday's draw.
Another non-league side making a name for themselves were Dover, conquerors of Gillingham in the first round, and victors over Aldershot in this.
An Adam Birchall 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.
York secured their passage with a 2-0 win at Darlington, while Huddersfield and Southampton both flexed their muscles with 6-0 and 3-0 wins over Macclesfield and Cheltenham respectively.
Luton will have a second bite of the cherry after a thrilling 2-2 draw at Charlton.
Joe Anyinsah gave Charlton an early lead but, an Andy Drury 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, while a double from veteran midfielder Tommy Miller helped Sheffield Wednesday to a 3-2 win over Northampton.
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.