Swansea capitalized on the 80th-minute sending-off of substitute Fabio Da Silva by scoring in the last minute through Wilfried Bony in a 2-1 win at United, the latest setback for David Moyes in his turbulent first season with the English champions.
United has lost four of its last six games at Old Trafford in all competitions and failed to reach the fourth round for only the second time in 30 years.
"We had another big game in 48 hours' time so we have to keep that in mind (but) no excuse," said Moyes, referring to the first leg of a League Cup semifinal against Sunderland on Tuesday. "We had a strong team out. Nearly every player out there was an international."
Like United, West Ham used a lineup full of reserves ahead of its League Cup semifinal against Manchester City on Wednesday, and the gamble backfired. The injury-hit Premier League struggler was crushed 5-0 at second-tier Nottingham Forest in the third round's biggest shock.
"We had a huge amount of problems in terms of the available members of the squad so I've got to keep them intact, that's a major priority," said West Ham manager Sam Allardyce, who was already under pressure with his team next to last in the league. "Many, many managers have changed the team in all divisions, but my changes had to be severe. I didn't want it to be but it had to be."
Chelsea and Liverpool played stronger lineups — and it showed. Second-half goals by John Obi Mikel and Oscar earned Chelsea a 2-0 victory at Derby, while Liverpool avenged last season's surprise defeat to third-tier Oldham in this competition by winning 2-0 at Anfield thanks to Iago Aspas' first goal for the club and an own goal by James Tarkowski.
That game also saw Liverpool manager Brendan Rodgers go up against his own son, Anton, who plays for Oldham and came on as a second-half substitute.
"I've seen Anton's life from when he was a young footballer and to see him run out there was a bit surreal really," Rodgers said.
Sunderland beat third-tier Carlisle 3-1 in the other third-round match featuring a Premier League team.
The fear factor about visiting Old Trafford has disappeared since Alex Ferguson left United last summer and Swansea was the latest team to take advantage, recording its first win at the home of the champions.
"Let's not kid ourselves, it's a really bad result," United midfielder Darren Fletcher said.
The Welsh side was helped by Moyes picking a shadow team that was missing injured strikers Wayne Rooney and Robin van Persie, as well as senior players Nemanja Vidic, Patrice Evra and Michael Carrick.
And Wayne Routledge put Swansea ahead in the 12th minute, running onto Alejandro Pozuelo's through ball and lobbing goalkeeper Anders Lindegaard. Javier Hernandez turned in Alexander Buttner's cross four minutes later for the equalizer, and Moyes said he was disappointed not to see his team kick on from then.
Fabio was given a straight red card for a studs-first lunge at Jose Canas, just four minutes after coming on as a substitute, and Bony made United pay by rising to head in Routledge's left-wing cross to cap an impressive performance.
"In my world, they are still a big team and for us to beat them, we still have to do a very good performance," Swansea manager Michael Laudrup said.
Allardyce fielded an unrecognizable starting XI featuring a host of youth-team players at The City Ground and they collapsed in the second half.
Djamel Abdoun's goal gave Forest a 1-0 lead at halftime before Jamie Paterson scored a hat trick and Andy Reid completed the humiliation with the fifth in injury time.
West Ham's lineup further highlights the FA Cup's increasing lack of appeal in the eyes of many top clubs nowadays but Allardyce made no apologies and knows there may be repercussions.
"There might be, who knows?" Allardyce said. "I'm not saying it won't happen unless I start to get results. I have got to get results, I know that."
The depth of Chelsea's squad shone through as Mikel headed home Willian's free kick in the 66th minute for only his fourth goal for the club in 300 appearances, before Brazil playmaker Oscar struck a fierce shot in at the near post five minutes later.
Chelsea will host Stoke in the fourth round while Liverpool must travel to Bournemouth or Burton.