Manchester United moved into the League Cup fourth round with a 2-1 win over Newcastle, while holders Liverpool fought back to seal a 2-1 victory at West Bromwich Albion on Wednesday.
United, looking to win the League Cup for the fifth time, made a host of changes from the side that won at Liverpool on Sunday.
However, they still fielded a strong side including Wayne Rooney, back from a month out with a thigh injury, and Darren Fletcher, who was starting for the first time in 10 months after recovering from a bowel condition.
United's Anderson broke the deadlock in the 44th minute when the Brazilian midfielder drove his shot past Rob Elliot.
Tom Cleverley put United further ahead in the 58th minute as the England midfielder curled home his first goal for United.
Papiss Demba Cisse came off the bench to reduce the deficit with a header four minutes later, but Sir Alex Ferguson's side survived a late barrage of Newcastle pressure to go through.
"I'm very pleased," Ferguson said. "Newcastle probably had a stronger team than us physically but we played some fantastic football and I think we deserved to win."
Rooney added: "I feel good, obviously it's always difficult in your first game back after a few weeks but it's great to get the minutes under my belt and hopefully that can benefit me."
At the Hawthorns, Brendan Rodgers' Liverpool made a terrible start when Australian goalkeeper Brad Jones spilled a free-kick and Gabriel Tamas pounced to score from close range in the third minute.
But Turkey midfielder Nuri Sahin equalised in the 17th minute with his first Liverpool goal, a long-range effort that Albion goalkeeper Ben Foster should have saved.
And Sahin ensured Liverpool, who made 11 changes from the United defeat, stole the victory when the on-loan Real Madrid star turned in Oussama Assaidi's cross in the 82nd minute.
"It was an outstanding performance," Rodgers said. "I'm not surprised as our performance level has been good all season. It's great to see the kids playing with confidence. We fully deserved the win."
Olivier Giroud finally ended his long wait to score his first Arsenal goal as the Gunners crushed League One strugglers Coventry 6-1 at the Emirates Stadium.
France striker Giroud, who had gone six games without a goal for his new club, got on the scoresheet when he converted a Francis Coquelin pass in the 39th minute.
However, the former Montpellier star wasted a chance to double his Gunners tally when his second half penalty was saved by Joe Murphy after Andrey Arshavin was fouled by Reece Brown.
But Arsenal remained firmly in control and Alex Oxlade-Chamberlain increased their lead after 57 minutes.
Russian winger Arshavin fired home six minutes later and Theo Walcott added the fourth in the 74th minute.
Callum Ball got one back for Coventry in the 78th minute, but Ignasi Miquel, Arsenal's young Spanish defender, responded with his first goal for the club two minutes later and Walcott netted his second in stoppage-time.
Arsenal's north London rivals Tottenham brushed aside League One side Carlisle with a 3-0 victory at Brunton Park.
Andre Villas-Boas made a host of changes to the Spurs side that beat QPR on Sunday, but still couldn't find a place for France goalkeeper Hugo Lloris, with Carlo Cudicini starting in goal.
That surprise decision didn't unsettle Villas-Boas's side, who took the lead in the 37th minute when defender Jan Vertonghen scored his first Spurs goal.
Andros Townsend doubled Tottenham's lead with a fine solo effort in the 53rd minute and Gylfi Sigurdsson completed the romp with his first goal for the club just before full-time.
Norwich paid tribute to John Bond, the club's second longest serving manager who passed away aged 79 on Wednesday, with a 1-0 win over League One side Doncaster at Carrow Road.
Reading came from behind to clinch a dramatic 3-2 win over QPR at Loftus Road.