Darren Fletcher captained Manchester United to a 2-1 win over Newcastle United, while Arsenal saw Olivier Giroud get off the mark in a 6-1 victory against Coventry City.
Nuri Sahin struck twice to give Liverpool a 2-1 victory over West Brom as Tottenham, Reading and Norwich also progressed into the next round.
Wayne Rooney also made a return from injury, with Anderson and Tom Cleverley giving the home side a 2-0 lead. Papiss Cisse reduced the deficit, but United held on for the win.
At the Emirates, Giroud opened the floodgates with the opening strike in the 39th minute. Alex Oxlade-Chamberlain thumped home a second goal, before Andrey Arshavin, Ignasi Miquel and a Theo Walcott brace made it an easy evening for the Gunners.
Jan Vertonghen, Andros Townsend and Gylfi Sigurdsson scored to help Spurs to a 3-0 win over Carlisle, while Norwich City edged past Doncaster 1-0.
Reading and Queens Park Ranger played out an entertaining match, with the Royals coming from behind twice to advance to the next round courtesy a 3-2 victory.
Liverpool manager Brendan Rodgers was delighted with his side performance after they fought back from going a goal down. "I think it was a symbolic night because it shows how fast we are moving as a group," Rodgers told reporters.
"How we have progressed from our first day of the season here, when we were a wee bit disjointed and players did perhaps not quite understand my methods and what I wanted.
"But the performance level has been high for a number of weeks. I think it's always exciting to see young players who have great technique. But what is important as well is that they understand how to fight. It was a wonderful performance against a good team.
"(West Brom manager) Steve (Clarke) has done a wonderful job here. He has made the team very hard to beat and obviously tonight he fielded an experienced team. For us to dominate the game like we did and to get the goals, and especially the second goal, it typified what we are all about.
"Overall the confidence on the ball and the ability to pass it and the courage to want it was very prominent with the players. It's really been the last three or four weeks when our tempo and rhythm and relentless possession has started to come through, so it was good to see and it was good to win."
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