Wayne Rooney returned from a monthlong injury absence as Manchester United eliminated Newcastle to set up a League Cup clash with Chelsea, while Liverpool relied on Nuri Sahin's first goals for the defending champions to advance on Wednesday.
Anderson and Tom Cleverley scored to give United a 2-1 victory as Rooney played for the first time since gashing his right thigh, completing 76 minutes at Old Trafford.
"It's been just over four weeks since I last played and I'm delighted to be back out on the pitch playing," Rooney said. "It was a good run-out for me and hopefully there's a lot more games to come. I feel good."
United midfielder Darren Fletcher made his first start for 10 months as he battles to overcome a chronic bowel complaint.
"It's been a long time so it's just good to be back, especially at Old Trafford and back in a winning team as well," Fletcher said.
Liverpool endured a nervy night, with Sahin scoring his second goal late on at West Bromwich Albion to secure a 2-1 victory after having equalized just before halftime. Just before the on-loan midfielder's winner, Jerome Sinclair became Liverpool's youngest-ever player by coming off the bench aged 16 years and six days.
In the fourth-round draw made after the match, Liverpool was drawn to face manager Brendan Rodgers' former club Swansea.
Arsenal will next face Reading after its 6-1 demolition of third-tier club Coventry was started by Olivier Giroud scoring his first goal since signing from Montpellier in the off-season.
"It was in everybody's mind that the sooner he gets it the better," Arsenal manager Arsene Wenger said. "Certainly in his mind, much more than in others' minds. That is positive of course. It was a good finish and he is a good finisher, Olivier.
"At the moment I believe he is looking for confidence again and that goal will help him."
