Richie Towell finally got his first senior goal for Brighton and Hove Albion, but his thunder was stolen by former Republic of Ireland U21 international Alan Power, who led Lincoln City to a shock FA Cup comeback victory.
Towell broke the deadlock after 24 minutes, producing a fine finish following a flowing Seagulls attack.
However the hosts - top of the Vanarama National League, the fifth tier of English football - had the Sincil Bank rocking thanks to a brilliant second-half recovery.
Dubliner Power drew the sides level from the penalty spot (below) after Glenn Murray was adjudged to have pulled Theo Robinson in the box, and on-loan Chelsea defender Fikayo Tomori's own goal turned the tiw on its head.
With Brighton pushing for an equaliser, Robinson punished them on the break to wrap up a terrific victory for the Imps.
Steven Defour's brilliant second-half chip capped a sixth straight home win for Burnley as they knocked Bristol City out.
The Clarets continued their impressive run at Turf Moor to move into the fifth round of the competition for the first time in six years with a comfortable 2-0 success over their Championship opponents, who had Irish international Callum O'Dowda in their starting line-up.
O'Dowda's old club Oxford United had a day to remember.
Championship high-flyers Newcastle were left to concentrate on their promotion bid after losing 3-0 at their League One opponents.
Kane Hemmings fired the Us in front two minutes into the second half.
Aleksandar Mitrovic had the chance to level from 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.
There was, though, no such trouble for Premier League leaders Chelsea, who saw off Brentford 4-0 at Stamford Bridge.
Willian opened the scoring on 14 minutes with a fine free-kick, before Spanish forward Pedro made it 2-0 before the break.
Substitute Branislav Ivanovic - who is reportedly set for a move away from Stamford Bridge before the end of the transfer window - added a third on 69 minutes and Michy Batshuayi scored a late penalty.
Manchester City ran out 3-0 winners at Premier League strugglers Crystal Palace.
Winger Raheem Sterling broke the deadlock just before half-time, with Leroy Sane and Yaya Toure, in the last minute, completing a comfortable afternoon in south London for Pep Guardiola's men.
Middlesbrough saw off League Two Accrington Stanley at the Riverside Stadium thanks to a 25-yard effort from Stewart Downing in the second half.
Huddersfield won 4-0 at Rochdale. German forward Collin Quaner, signed from Union Berlin, scored on his debut before a penalty from Isaiah Brown and a late double for Michael Hefele secured the Terriers' place in the last 16.
Blackburn beat Blackpool 2-0, as the visitors finished with 10 men at Ewood Park.
Sam Gallagher put Rovers ahead on nine minutes, with winger Elliott Bennett doubling the lead in the 22nd minute before Blackpool midfielder Kelvin Mellor collected a second caution midway through the second half.
