West Ham were dumped out of the FA Cup by Championship side Bristol City 1-0 on Tuesday as Newport County set up a dream fourth-round tie against Manchester United.
Tommy Conway scored the only goal at Ashton Gate after less than three minutes to ensure the Hammers' 44-year wait to lift the FA Cup will go on.
Conway, who also scored to secure a replay when the sides met at the London Stadium, pounced on a short back pass from Konstantinos Mavropanos to round Lukasz Fabianski and slot into an unguarded net.
"I've been coming here since I was seven and to get the winner is unbelievable," said Conway.
"It's the best (crowd) I've seen it in a while and to send them home happy is unbelievable."
David Moyes' men missed the threat of the injured Jarrod Bowen and Lucas Paqueta and Mohammed Kudus, who is away representing Ghana at the Africa Cup of Nations.
The visitors had to play almost the entire second half a man down after Said Benrahma was sent off for kicking out at Joe Williams in retaliation to a late challenge on him.
Tomas Soucek came closest to forcing the game to extra time when the Czech's volley forced Max O'Leary into a flying save.
Bristol City will next face Blackpool or Nottingham Forest in round four.
League Two Newport ended the run of non-league Eastleigh with a 3-1 win to earn the right to host the Red Devils on January 28.
Brentford boss Thomas Frank got exactly what he did not want as his side were forced to extra time before losing 3-2 to Wolves.
Frank questioned the need for replays as both sides saw their two-week winter break shortened by the extra game.
Twice the Bees went in front through former Wolves defender Nathan Collins and Neal Maupay.
But Nelson Semedo and teenager Nathan Fraser hit back for Wolves and Matheus Cunha's penalty won the game in extra time.
Wolves will now face local rivals West Brom in the last 32.
Luton edged out League One Bolton to progress 2-1 despite falling behind to Dion Charles' early strike.
Tahith Chong quickly levelled for the Premier League side before Chiedozie Ogbene grabbed the winner.
Birmingham also came from behind to beat Hull 2-1 thanks to Koji Miyoshi's 94th-minute winner.
