Youthful United prove too good for Newcastle
Holders Liverpool also rang the changes and came from behind at West Bromwich Albion to win 2-1 thanks to two goals from Nuri Sahin.
Tottenham Hotspur beat Carlisle United 3-0 and their North London rivals Arsenal strutted into the last 16 with a 6-1 drubbing of third tier Coventry City.
United made 11 changes from the team that started against Liverpool in the Premier League on Sunday with Wayne Rooney returning after injuring his leg four weeks ago and midfielder Darren Fletcher making his first start for 10 months.
With a string of defensive injuries, manager Sir Alex Ferguson turned to youth with Alex Buttner, Marnick Vermijl, Scott Wootton and Will Keane tasked with keeping the Newcastle forwards at bay.
It is 40 years since the north-east club last won at Old Trafford and their chances of causing an upset were reduced when midfielder Anderson broke the deadlock with a spectacular left-foot strike from 25 metres just before halftime.
The Brazilian has struggled to force his way into the first team reckoning this season but was a driving force as United took the game by the scruff of the neck.
The hosts made their superiority tell in the second half when midfielder Tom Cleverley, who missed a gilt-edged chance before the interval, doubled the lead with a precise right-foot strike from the edge of the area.
Newcastle hit back when substitute Papiss Cisse headed home from close-range for his first goal of the season and he went close to levelling when he volleyed an overhead-kick against the crossbar.
"Newcastle had a stronger team than us physically. We played fantastic football and I think we deserved it," United manager Ferguson told Sky Sports.
"Anderson's was a great strike. The second is a great bit of football. Cisse is a terrific player. Our defence handled it well."
Liverpool also fielded a completely different team and fell behind on three minutes when West Brom's Gabriel Tamas finished from close range after a mistake from the visitors' stand-in keeper Brad Jones.
Playmaker Sahin, on loan from Real Madrid, levelled with a speculative shot from distance and struck again late in the second half when he converted Oussama Assaidi's cross at the back post.
Forward Jerome Sinclair became the club's youngest ever player at 16 years and six days when he came on as a second-half substitute.
"It's congratulations to Jerome Sinclair. Our future is bright with the young players. The style and definition of our game is improving all the time," said Liverpool manager Brendan Rodgers whose name was sung Liverpool fans at the final whistle.
"It's great to see the kids playing with confidence. We fully deserved the win. For me it's about talent irrespective of age. We've got a small squad. It's a club where young players are going to get a chance."
Arsenal named a strong attacking line-up with Andrei Arshavin, Theo Walcott, Alex Oxlade-Chamberlain and Olivier Giroud all starting.
Giroud, who joined from Montpellier in June, enjoyed a mixed night, scoring his first goal for the club with a neat finish to before failing to find the net with a penalty.
It proved to be academic as Oxlade-Chamberlain, Arshavin, Walcott (2) and Ignasi Miquel completed the rout.
For Tottenham there was no place in the starting line-up for France keeper Hugo Lloris, signed for 12 million-pound from Olympique Lyon, as third-choice Carlo Cudicini was preferred in goal.
Tottenham took the lead against their third tier opponents when Gylfi Sigurdsson's cross was headed home by defender Jan Vertonghen.
Andros Townsend added a second with a run from the halfway line and a low shot into the net and Sigurdsson rounded off the scoring with a header.
Reading came from 2-1 down to beat Queens Park Rangers 3-2 in an all-Premier League match and Norwich City won 1-0 at home to Doncaster Rovers.