London - Wilfried Bony has snatched a dramatic last-minute winner as Swansea City heaped fresh misery on Manchester United with a shock 2-1 success in the FA Cup third round on Sunday.
Eleven points off the pace in the Premier League, where they have already lost six games, United crashed out at the first hurdle in the FA Cup to give beleaguered manager David Moyes even more problems.
To compound matters, United's injury list swelled further after Rio Ferdinand had to go off with a knee injury, while Fabio da Silva was sent off shortly after coming on to replace him.
"We were a bit unlucky to lose, but we probably didn't do enough to win it in the end," said Moyes, whose side visit Sunderland in the League Cup semi-finals on Tuesday.
"We made some opportunities, (but) not enough. When we went down to 10 men, we just needed to see it out and at least take a replay if that was what had to come about, but we didn't quite get that far."
In a game preceded by a minute's applause for late Portugal great Eusebio, who died on Sunday, Swansea took a 12th-minute lead through Wayne Routledge, who cantered onto a pass from Alejandro Pozuelo to lob Anders Lindegaard.
The hosts equalised four minutes later, Javier Hernandez volleying in a cross from Alexander Buttner, but they could not find a second goal.
Ferdinand had to hobble off due to injury late on and his replacement, Fabio, was sent off for a high challenge on Jose Canas shortly after coming on.
Worse was to follow at the death, with Routledge lifting a cross into the box from the left and Bony powering home a near-post header to add a new chapter of disappointment to the tale of United's unravelling season.
West Ham United also fell in the third round on Sunday, crashing to an embarrassing 5-0 defeat at second-tier Nottingham Forest, but Chelsea and Liverpool both progressed against lower-league opponents.
Chelsea beat in-form Championship side Derby County 2-0, with Liverpool avenging their shock defeat by third-tier Oldham Athletic in last season's competition with a 2-0 success at Anfield.
Chelsea enjoyed the best of the first half against Derby at Pride Park but they had to wait until the 66th minute before making the breakthrough against former England manager Steve McClaren's side.
Eden Hazard's trickery wide on the left yielded a free-kick and from Willian's wicked, in-swinging cross, John Mikel Obi glanced home a header to mark his 300th Chelsea appearance with his fourth goal for the club.
Oscar got on the score-sheet shortly afterwards, gathering a pass from Hazard and beating Lee Grant at his near post with a powerful shot.
Chelsea manager Jose Mourinho highlighted the importance of Mikel's goal, saying: "It was important for us because we were dominating and dominating, creating and creating, but the goal was not arriving. It was like the winning goal."
Liverpool will visit either Bournemouth or Burton Albion in round four after seeing off Oldham, who stunned Brendan Rodgers's side 3-2 at Boundary Park in the fourth round last season.
Iago Aspas, a close-season signing from Celta Vigo, broke the deadlock in the 54th minute by dispatching a cross from Raheem Sterling to claim his first goal for the club.
Liverpool did not secure victory until Oldham's James Tarkowski put through his own goal with eight minutes to play.
West Ham became the second Premier League team to be eliminated by lower-league opposition in this season's competition when they were crushed 5-0 by Championship side Forest at the City Ground.
A day after Aston Villa fell to third-tier Sheffield United, West Ham were undone by a 14-minute hat-trick from Forest forward Jamie Paterson, sandwiched by an early Djamel Abdoun penalty and a late Andy Reid strike.
West Ham manager Sam Allardyce made nine changes to his starting XI and gave debuts to three young players, but he told ITV: "What choice did I have? I don't think I had one.
"I make the decisions for the benefit of everyone at the football club. We have a huge amount of problems in terms of available players."
Sunderland overcame third-tier Carlisle United 2-1 at the Stadium of Light to take their place in round four.
Adam Johnson put Sunderland ahead with a fine 34th-minute free-kick and then supplied the cross from which Sean O'Hanlon put through his own goal after Matty Robson had levelled the scores.
A 90th-minute strike from 20-year-old French midfielder El-Hadji Ba completed victory for Gus Poyet's men.Collated English FA Cup third-round results on Sunday:
Derby County 0 Chelsea 2 (Mikel 66, Oscar 71)
Liverpool 2 (Aspas 54, Tarkowski 82-og) Oldham Athletic 0
Manchester United 1 (Hernandez 16) Swansea City 2 (Routledge 12, Bony 90)
Nottingham Forest 5 (Abdoun 12-pen, Paterson 65, 71, 79, Reid 90+1) West Ham United 0
Port Vale 2 (Tomlin 15, Pope 36) Plymouth Argyle 2 (Reid 51, Purrington 73)
Sunderland 3 (Johnson 34, O'Hanlon 50-og, Ba 90) Carlisle United 1 (Robson 43)
Arsenal 2 (Cazorla 31, Rosicky 62) Tottenham Hotspur 0
Aston Villa 1 (Helenius 75) Sheffield United 2 (Murphy 20, Flynn 81)
Barnsley 1 (O'Brien 19) Coventry City 2 (Moussa 78, Clarke 89)
Blackburn Rovers 1 (Dann 55) Manchester City 1 (Negredo 45)
Bolton Wanderers 2 (Ngog 10, Beckford 51) Blackpool 1 (Barkhuizen 45)
Bournemouth v Burton Albion -- postponed (waterlogged pitch)
Brighton and Hove Albion 1 (Crofts 32) Reading 0
Bristol City 1 (Emmanuel-Thomas 85) Watford 1 (Murray 84)
Charlton Athletic v Oxford United -- postponed (waterlogged pitch)
Doncaster Rovers 2 (Forrester 72, Wakefield 90) Stevenage 3 (Zoko 49, Hartley 65, Charles 90)
Everton 4 (Barkley 35, Jelavic 44, 68, Coleman 76) Queens Park Rangers 0
Grimsby Town 2 (Hannah 25, Disley 62) Huddersfield Town 3 (Norwood 51, Paterson 86, Thomas 90-og)
Ipswich Town 1 (McGoldrick 38) Preston North End 1 (Davies 42)
Kidderminster Harriers 0 Peterborough United 0
Macclesfield Town 1 (Williams 72) Sheffield Wednesday 1 (Johnson 25)
Middlesbrough 0 Hull City 2 (Mclean 10, Proschwitz 61)
Newcastle United 1 (Cisse 62) Cardiff City 2 (Noone 73, Campbell 80)
Norwich City 1 (Snodgrass 45) Fulham 1 (Bent 40)
Rochdale 2 (Hogan 45, Henderson 84) Leeds United 0
Southampton 4 (Clyne 22, Lambert 28, Rodriguez 66, Lallana 73) Burnley 3 (Vokes 51, Ings 57, Long 87)
Southend United 4 (Corr 22, Atkinson 45, Timlin 57, Leonard 90) Millwall 1 (Woolford 64)
Stoke City 2 (Jones 16, Adam 55) Leicester City 1 (Nugent 77)
West Bromwich Albion 0 Crystal Palace 2 (Gayle 23, Chamakh 90)
Wigan Athletic 3 (Espinoza 18, Gomez 27, McManaman 65) Milton Keynes Dons 3 (Reeves 45, 45, Bamford 84)
Yeovil Town 4 (Hayter 12, 60, Grant 49, Moore 90) Leyton Orient 0