Manchester United battled past a resurgent Newcastle to earn a Capital One Cup fourth round tie at Chelsea.
Anderson scored when he marched towards the visitors' defence just before half-time and fired into the bottom corner.
England midfielder Tom Cleverley, 23, made it 2-0 from 18 yards with his first Manchester United goal.
Papiss Cisse's introduction almost sent the game to extra time when he scored with a close-range header and hit the bar with an overhead effort.
The Senegalese striker was rested alongside a number of other Newcastle first-teamers, but he made a real impact by scoring his first goal of the season two minutes after coming on and Dan Gosling could also have equalised with a tame late effort.
Javier Hernandez also hit the bar after Cisse's goal, but the hosts were hanging on as Alan Pardew's side finished strongly.
Wayne Rooney returned for the home side, after suffering a nasty leg injury against Fulham a month ago, and Darren Fletcher was made captain on his first start in 10 months - but Cisse's introduction put pressure on a young back four that had just two senior appearances between them.
For most of the game, debutants Scott Wooton and Marnick Vermijl, alongside Michael Keane and Alex Buttner, coped well, with Buttner impressing down the left.
Manchester United boss Sir Alex Ferguson will be content they came through this test without any serious problems and the performances of Anderson and Cleverley, and an understandably tiring Fletcher, would also have pleased him.
Before their goals, both midfielders could have scored - but Newcastle keeper Rob Elliot saved the Brazilian's effort while Cleverley was inches wide of the post.