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.
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.
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.