The Imps, who beat Ipswich Town after a replay in the last round, had to come from behind after Richie Towell put the Championship side ahead on 24 minutes.
The non-league outfit were then handed a way back into the tie on 57 minutes when Glenn Murray grappled with Theo Robinson, and Alan Power converted the spot-kick.
An own-goal from Seagulls defender Fikayo Tomori then put the Non-League side in front on 62 minutes before Robinson added a third on the break.
The afternoon of unexpected results had started with Wolves' win at Anfield in the lunchtime kick-off.
The SkyBet Championship side were ahead after just 52 seconds when Richard Stearman glanced in a free-kick at the far post before Andreas Weimann doubled the advantage just before half-time after a swift counter attack.
Divock Origi pulled a goal back for Jurgen Klopp's much-changed Liverpool side with five minutes left, but Wolves held out for the closing stages to claim another Premier League scalp after knocking out Stoke City in the Third Round.
Meanwhile Championship high-flyers Newcastle United lost 3-0 at League One Oxford.
Kane Hemmings fired the U's in front two minutes into the second half - Aleksandar Mitrovic then had a chance to level with a penalty on 67 minutes, but the Serbian's spot-kick was saved by Simon Eastwood.
With nine minutes left, Curtis Nelson headed home from a corner and Antonio Martinez nodded in a late third.
Premier League Tottenham Hotspur also needed two late goals to beat League Two outfit Wycombe Wanderers 4-3 at White Hart Lane.
Wycombe went ahead on 23 minutes when captain Paul Hayes fired a volley past Michel Vorm before stunning the home side again by converting a penalty in the 36th minute.
Son Heung-min pulled Spurs back into the tie on the hour and Vincent Janssen levelled when the Dutchman slotted in a 65th-minute penalty.
However, the Chairboys - fifth in League Two - silenced the White Hart Lane faithful once again as Garry Thompson headed home with just seven minutes left.
England playmaker Dele Alli, though, dashed dreams of a massive FA Cup upset before Son completed a dramatic victory in stoppage time.
There was no such drama for Premier League leaders Chelsea FC at Stamford Bridge though, expertly seeing off West London rivals Brentford 4-0 while Manchester City ran out comfortable 3-0 winners at Crystal Palace.
Middlesbrough saw off League Two Accrington Stanley at the Riverside Stadium with a 25-yard effort from Stewart Downing; Burnley beat Bristol City 2-0 at Turf Moor and Lancashire rivals Blackburn Rovers beat Blackpool 2-0.
In Saturday's late kick-off, Theo Walcott scored a hat-trick as Arsenal romped to a 5-0 win at Southampton.
Both sides made expected changes, but it was the Gunners who looked sharp as Danny Welbeck netted an early double, his first goals since a return from a serious knee injury, to put the visitors 2-0 up inside 22 minutes.
Walcott, who had been out himself since before Christmas because of a calf problem, took home the match ball as manager Arsene Wenger watched from the stands for the start of a four-match touchline ban.
FA Cup 4 Round Results, Friday January 27-Saturday January 28
Derby County 2-2 Leicester City (Friday)
Liverpool 1-2 Wolverhampton Wanderers
Burnley 2-0 Bristol City
Chelsea 4-0 Brentford
Crystal Palace 0-3 Manchester City
Blackburn Rovers 2-0 Blackpool
Lincoln City 3-1 Brighton &Hove Albion
Middlesbrough 1-0 Accrington Stanley
Oxford United 3-0 Newcastle United
Tottenham Hotspur 4-3 Wycombe Wanderers
Southampton 0-5 Arsenal
Today's fixtures include Millwall v Watford (Noon); Fulham v Hull City (12.30pm); Sutton United v Leeds United (2pm) and Manchester United v Wigan Athletic (4pm).
The draw for the 5th Round will take place on Monday, January 30 at 7.20pm.