The League Two side bridged a gap of 59 positions in English football's standings to stun Wigan with a Stephen Hunt header and an own goal by Gary Caldwell - both goals coming in three minutes in the second half.
Another fourth round replay also produced a shock with Championship Crystal Palace, who were recently plunged into a relegation dogfight after a 10-point deduction for going into administration, ousted top flight Wolverhampton Wanderers 3-1 at Selhurst Park.
Danny Butterfield netted a second-half hat-trick for Palace who will take on Aston Villa for a place in the quarter-finals.
"We are fighting together and we showed people around the country tonight that we are far from dead," Palace manager Neil Warnock told ITV Sport.
Notts County, who last week secured investment to ward off administration after they were issued with a High Court winding up order, will get another crack at Premier League opposition in the fifth round against Fulham.
County began the season with lofty ambitions after former England manager Sven Goran Eriksson became director of football but hopes of a rapid rise through the divisions after the club's takeover by a Middle East consortium have petered out.
Off-field financial concerns - the owners who appointed Eriksson have left the club - and the departure of two managers as well as the ill-fated signing of former England defender Sol Campbell have made it a chaotic season at Meadow Lane but a first FA Cup victory over a top flight side since 1991 is a welcome boost.
Hunt put the visitors ahead with 15 minutes remaining, heading in a corner, before Caldwell sealed Wigan's fate when he headed into his own net while attempting a clearance.
