At the end of a week that saw the Premier League giants fire their head coach Ruben Amorim, the defeat has likely consigned United to another trophyless season and was greeted with loud jeers from the home crowd.
Welbeck scored what proved the decisive goal in the 64th minute - meaning Benjamin Sesko's late header was only a consolation in the third round match for United, who were under caretaker boss Darren Fletcher for the match.
United have now exited both domestic knockout competitions at the earliest possible stage this season, following the humbling loss to fourth-tier Grimsby in the English League Cup.
United's only chance of silverware this term is the Premier League, which would require a remarkable turnaround with the 20-time champions currently seventh in the standings and 17 points behind leader Arsenal with 17 games left.
"It's probably not what fans want to hear about Manchester United because they've been winning cups and challenging for the Premier League," Fletcher said.
"Don't waste the season. That would be the challenge that I would set. That's the challenge that probably the players feel like they need to achieve this year."
It was a different story for Arsenal, who advanced earlier on Sunday with Gabriel Martinelli scoring a hat trick in a 4-1 win at Portsmouth, for whom young Socceroo Adrian Segecic played 73 minutes before being replaced.
Martinelli's treble helped the Premier League leaders come back from going a goal down to the second-tier Championship team inside three minutes when Colby Bishop hit the opening goal at Fratton Park, but the lead only lasted five minutes after Andre Dozzell scored an own-goal.
Martinelli put the visitors ahead with a flicked header in the 25th. He slid in for his second six minutes after the break and headed in his hat-trick goal in the 72nd. It was the first time the Brazilian had scored a hat trick for Arsenal.
"It's always tough to go into these places, especially in the manner that we started the game, conceding the early goal, but we managed to turn things around so I'm very happy," said manager Mikel Arteta.
Top-flight Leeds were also behind to Championship opposition, but recovered from 1-0 down to beat Derby 3-1 at Pride Park.
Third-tier Mansfield pulled off an upset to beat Championship side Sheffield United 4-3 and Norwich routed Walsall 5-1, with Jovon Makama scoring a hat trick. Norwich head coach Philippe Clement later said that U.S. international Josh Sargent refused to play in the game.
Relegation-fighting West Ham needed extra time to beat QPR 2-1. Valentin 'Taty' Castellanos' goal saw Nuno Espirito Santo's team end a 10-match winless run.
West Bromwich Albion beat Swansea 6-5 on penalties following a 2-2 draw after extra time, Australia's Cameron Burgess a used substitute for the Swans.
Hull won 4-3 against Socceroos defender Lewis Miller's Blackburn on penalties after a 0-0 draw.
22°C