Manchester United were knocked out of the FA Cup after a 2-1 loss at home to Swansea, the Welsh side's first win at Old Trafford.
Wilfried Bony scored the winner in the 90th minute after Javier Hernandez had cancelled out Wayne Routledge's 12th-minute opener.
Earlier, Chelsea eased to a 2-0 win over Derby in their FA Cup third-round match.
Mikel put them ahead after 66 minutes, the Nigeria international getting on the end of a Willian set-piece to head in his fourth goal for Chelsea in almost 300 appearances.
Oscar added a second from the edge of the area to make the game safe and set up a fourth-round tie at home to Premier League Stoke City.
Meanwhile, Iago Aspas' first goal for Liverpool and an own-goal by James Tarkowski helped the Reds overcome Oldham 2-0.
West Ham United boss Sam Allardyce defended his team selection after his much-changed side were thrashed 5-0 by Nottingham Forest in the day's early kickoff.
Allardyce made nine changes from the team which lost to Fulham in the Premier League last weekend.
"What choice (in terms of team selection) did I have? I don't think I had one," he told reporters.
"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.
"We have a League Cup semi-final against Manchester City and the main priority is to get to Wembley. My changes had to be severe today, I didn't want it to be."
West Ham were undone by goals from Djamel Abdoun and Andy Reid either side of a second-half hat-trick from Jamie Paterson to leave Allardyce facing fresh questions about his future.
In the other game, Sunderland scored a convincing 3-1 win over Carlisle.
Sunderland were briefly made to sweat when Adam Johnson's opener was cancelled out by Matty Robson just before halftime.
The second half was just five minutes old however, when a comical own goal restored the Premier League side's lead, with Sean O'Hanlon sliding in to divert Johnson's cross into the net.
El Hadji Ba made the game safe on 90 minutes when he sidefooted home from close range.